Over a century old doesn't matter if it's never spoken of and not pursued again. It was technology that was abandoned over a century ago not technology that was developed for a century. Development outright stopped. Without Stamets and Tartigrade DNA, like has been said before, the technology went nowhere. And what little they could do was classified. This is just a technology that didn't take off. Starfleet couldn't figure out how to operate it without Tartigrade DNA. No one cracked that code. And, again, no one knows about it.
Janeway doesn't know about any Spore Drive because she was never told about any Spore Drive and if she tried to look it up in the Federation Database, it wouldn't be there.
The whole point of suppressing knowledge about Discovery and the Spore Drive was to prevent anything like Control, or a re-emergent Control, or a Control that wasn't as neutralized as they thought, from ever gaining information from Discovery. You'd think they'd make it impossible (or at least extremely difficult) to find out anything about it.
So the fact that Janeway doesn't know anything means that Section 31 and Tyler were successful and that Starfleet Command actually listened to Spock's suggestion. And by Starfleet Command, I don't mean the whole of Starfleet Command. I mean that one Admiral they spoke to. Classified means classified. I doubt even Admiral Paris knows about the Spore Drive.
And the Spore Drive probably won't come up on Picard.
"But the Klingons!" They were divided. They weren't organized until L'Rell, who I think it's safe to say never found out about how the Spore Drive worked and didn't seem curious about finding out how after The War ended. The Klingons, being as they are, moved on to the next thing to focus on. By the time L'Rell's Chancellorship ended (whenever that happens to be), the Klingons had moved way passed it. They just didn't care about this thing they couldn't duplicate. They -- or more accurately, S1 L'Rell -- wanted to capture Discovery as a trophy, but the moment passed.
The Klingons fought for nine whole months after Discovery disappeared into the Mirror Universe. So Disco's stock in the opinion of the Klingon Empire probably went down during those months because it wasn't around anymore. And they came close to winning. The only reason the war ended -- from their point of view -- is because L'Rell told them to stop and she had the weapon to back up her demand. So they didn't surrender to the Federation. They pledged to served L'Rell, who was stronger than them. It was a way to stop the war that they'd accept. So they didn't see Discovery as a tactical advantage because they were able to do just fine without it. And you can bet they're macho enough that they want to fight the toughest battles possible. They'd only care about the Spore Drive if the Federation were still using it, so they could one up them. If the Federation isn't using it, they're not using it. They don't care.