Hmm I don't see my production numbers going up when clicking convery
Do you have a stockpile of obsolete equipment to convert? You need to mark the older type as obsolete in the right-hand list, along with checking the "convert" circle in the lower left corner of the production line for the new type. If the older type isn't marked obsolete, the stockpile will keep issuing those planes to keep units fully equipped, and there won't be many to convert to a newer type.
When there are no planes to convert, a "convert" line for a newer variant will just produce the new variant normally, from scratch. When those planes get issued, you'll get a few to convert when they're issued to replace older variants -- but those quickly get converted and sent back out. So, without a backlog of old stuff, you only get as many to convert as your new production manages to replace. This is a small improvement over the full production time, as the line converts planes every time it makes a new one from scratch, but there aren't many planes with which to see the benefit.
Also, "conversion" means that the new type has to have been created as a variant of the previous type. That is, for the sake of example, suppose you have a newly-researched base fighter type. You make some ("Ftr"). You get some xp, and create a variant, ("Ftr A"). You get some more xp, and go back to Ftr and create a new variant, "Ftr B". In this case, you can't convert Ftr A to Ftr B, because B isn't a variant of A. More commonly, you'd go to Ftr A and create a new variant, Ftr B, as that lets you keep the improvements to A. But sometimes, people might specialize their planes in two different directions (guns vs agility, or a long-range version for large air zones).
In a sample save I checked, checking the "convert" circle gives me a boost of about 64% in the production rate (15.86 to 25.99 planes per day, for that particular example)
