Espionage feels weak for a few reasons. first, its micro-intensive, making the player have to engage with the subsystem a lot to get the most out of it. It is resource intensive, which is okay, when you hit mid-game and have a lot less to sink influence into but during the early game where spycraft may be the most important (as you know the least about enemy builds at this point) you are far better off sending your envoys to serve on first contacts which generate influence, and putting said influence into map expansions.
This then wraps into a lot more effort and cost having to be sunk in to spy on rivals and more hostile powers than friendlier ones who can give you reasonable amounts of intel from embassies and one or two pacts. personally, I never had to use the steal map option once as most of the time and friendlier empires will fill it in for me and if not one spy ship can resolve any missed points on the map.
The envoys also feel less like leaders and more like a resource, which while reasonable as people didn't like using officials for it, this ends up making their impact far more minimal.
Rather than how well you can get in being directly tied to their relation to you and their Diplo statuses (Closed borders, primary species only, etc) one of the big factors should be crime and stability, the less stable a planet/system/empire is the easier it is to infiltrate. on that I also think the player can choose where to target, each one being more influential than the last but at the cost of risk
-Planet or system, the easiest. for when you want to do a quick job or to target a specific leader. short time to invest and has fairly easy results, the defender in a way shouldn't need to worry about this as well as any issues can be resolved easily. much like crime issues spurred by a spy on these levels can be reigned in with soldiers or Enforcers so long as a planet is properly managed.
-Sectors, Should be treated as the default, middling in challenge the goal here is affecting a larger scale or planetary issues en-mass, here you can incite sector based revolts, convince systems to join you, push for piracy, and other things that can weaken an area for conquest or distract an enemy. nothing deliberating but limiting
-Empire, this is espionage at the highest degree, it should be hard for an empire to do so unless they're built for it. at its top end it shouldn't just be crippling an opponent or weakening them but actively pushing them to align with you, this can include getting assets as council leaders, shifting research focuses, and cultural changes. if you are doing stuff at this level it should feel very cold war-like.
I am personally fine with envoys as a concept but they should also go back to being leaders, a lot of the stuff written for them is leftovers from when they were. the issue was making them officials opposed to their own leader type. officials should have some expansion in use, though that is a separate topic; envoys however should have their range a bit more expanded to cover this and to streamline espionage options.
Envoys as they are tossed to improve diplo, go to a pan-galactic group (federations, GC,) or sent to spy. Each of these is fine as diplomats tend to also serve as espionage assets in the real world but this also goes into the cost-weight that espionage suffers from, most of the time you will get better results in improving relations or sending envoys to your federation than sending them to the GC or to commit espionage acts.
With this, I would suggest if an envoy is sent to an empire at any level (Planet/Sector/Empire) they do double duty to maintain or shift relations, just at the cost of possible efficiency, and have the player choose which one they rather focus on rather than committing to one or the other.
Envoys sent to Pan galactic groups in turn will also serve as espionage assets on most if not all members just at a significant delay to efficiency and locked to more surface-level acts. (The idea is that these envoys can serve as more of a bridgehead to save you time digging into other empires, as opposed to new espionage acts starting from zero you'd start at say ten or fifteen for example). on a federation and vassal end, outside the standard federation, the other members should not know everything about each other, just that intelligence gain would be much easier due to integrated politics. weaker members of a group should be able and try to build assets in secret, especially if they're not fond of their current dynamic or wish to get a higher position.
Envoys as governors will also focus on species relations and counter-espionage; while ideally, each governor type would deal with it to a degree via traits they would be the ones more built to root out localized agents without the player having to worry too much about the hunting of enemy envoys.
Finally, I think there should be a new classification of holding that is hidden from an empire. These Clandestine holdings are the most numerous and any empire can establish them if they have enough infiltration in another at the cost of significant damage to relations and destruction of the holding if discovered. Clandestines will also be used by criminals or pirates if regional stability is low enough. Empires can also establish Clandestine holdings on their own planets to deal with certain issues, boost espionage effects, or generate more "positive" crime at the cost of pop happiness and stability if revealed.
Clandestine Holdings have 4 flavours
-Blacksites, these are the ones players develop in personal systems, other empires, or in vassals, they can serve as more powerful variants of vassal holdings and other stability-boosting buildings and counter-espionage internally, and in vassals and other empires, they can serve as flat boosts to espionage effects as well. the caveat is that they can be lost far more easily than any other holding you can build
-Criminal holdings, self self-explanatory however players should be able to found them, and like Blacksites serve to boost espionage just to a lower degree.
-Hidden Nodes, this is a gesalt-only flavour and allows gestalt pops to be established in non-gesalt empires (ideally to give a hivemind invasion/ secret conversion feel)
-Rogue operations, these are ones internal AI may establish in preparation to rebel or if the the planet/ sector is unstable enough to generally siphon off income from the system into its governor pocket, a bit of a transitory phase between Criminal holdings and Blacksites.
Clandestine Holdings like default criminal jobs will siphon workers to fill them but their exact job will be hidden till the holding is discovered. upon discovery, the crime generated (if any) will be lowered and you gain the option to destroy it. all these holdings will still give some benefit to the host empire but it is worthwhile to keep at the risk of stability. Every Clandestine Holding on a planet has a higher chance to be found, based on enforcer, soldiers, and governor type. Blacksites will also give a CB to the empire that built it to remove any others they have Criminal holdings if founded by an empire have plausible deniability and can only be destroyed (unless it's a criminal Megacorp).
TDLR; Envoys the base of diplomacy and Espionage have little presence despite being one of the core mechanics of these systems.