Don't think so. IF this was true (kinda doubt it tbh) it was probably just to get Messi away from Nikes biggest flagship. They have the personal deal with him but their biggest competitor still had his face everywhere because of Barca so would make sense to try to "steal" him. And Chelsea and Bayern were the biggest Adidas clubs at that point afaik, besides Real.
When it comes to Bayern, there aren't any reliable infos of Adidas being involved in deals as far as i'm aware. Like sometimes it's rumored, or players sign new sponsoring deals etc but nothing about Adidas actually paying for transfers or anything like that. Only one i can remember is them paying the signing fee for Claudio Pizarro but that was like 15 years ago
I personally don't think they really help with transfers, i think it's more about their personal deals with players that may help to attrack players so both sides can profit. But that's something that nike probably also could do or does for us, because at this point they sponsor us for 20 years and we recently got this huge contract until 2026 so that shouldn't be a problem. But just like signing fees, and agent fees etc these are the things we hardly ever hear anyway.
To stay on topic here...i think Pepe could fit them quite well. They need a RW that can score some goals so he should be good for that. There are different numbers reported, i think straight up 80M would be too much but like 50-60 + some boni would be ok in todays market. Don't think he's gonna become like undoubtedly world class, but can turn out quite good. After all thats what you can expect from a winger of that price range, that's why we had to pay up to 130M for Dembele lol