An older although similar bug report:
Installing new fonts don't automatically list in Illustrator unless I restart the App
http://illustrator.uservoice.com/forums/601447/suggestions/34045294

After recent updates, when a font is installed while the program is in use, it does not appear in the list. You need to close the program and open it again. This wasn't a problem before.

Hello Egor,
The font management program I use is called MainType 8.0 / (high-logic.com). I've been using MainType for over eight years now. But this problem is new. I first noticed it a few weeks ago after an update.
I'm using a PC with Windows 11. The system has the fonts supplied with Windows installed, and I activate or install fonts when I need them for a project. These are located in a folder on the "C" drive. These are mostly OpenType fonts these days.
Even if I install a font directly from C, I still have to close and reopen the file used in Illustrator. Only then is the font active. That's frustrating.

Andreas, the team would need to know what font management program are you using, where are these fonts located, what are these fonts exactly? How many of these do you have installed?
If you install these using the default method (with putting files directly into c:\Windows\Fonts\) — do these get added faster?

Personally, I’ve been having a similar problem for decades now. Sometimes these do get added 'fast' (less than 10 seconds), sometimes it goes up to 30 seconds. Most of times Ai goes unresponding while these do get added. And yes, I do recall this behavior, with not seeing added fonts at all — but it stopped maybe a half a year ago...
Working on Mac feels a lot faster, but I never had the same amount of active fonts there.

In the past, when I activated or installed one or more new fonts with my font management program, Illustrator would indicate after a few seconds that the fonts had been recognized.
If I do that today, I have to restart Illustrator so that the fonts are displayed as active in the program.
Not nice.
Can anyone help or is this a bug within Illustrator?

My apologies for not being thorough. I realized I could still test this issue even with the warnings that popped up. It does indeed work to activate and deactivate fonts; rather quickly actually. Thank you for your patience and efforts on this.

I just received a reply from Extensis. They do not support any Beta versions of Illustrator and I'd have to wait for a fully released future version to test this.

I'm a nobody-regular-user and as such you'll probably need some corporate leverage to get Extensis to help you test Betas.

I had to uninstall other versions of Illustrator after installing the Beta version so that Extensis Connect wouldn't automatically install plug-ins for the old versions. After restarting both the Beta Illustrator and Extensis Connect, AI says there is not a compatible Extensis plug-in and Extensis doesn't show an installed plug-in for any Illustrator app. I'm guessing that means Extensis needs to update their plug-in before this can be tested completely.

Been struggling for about a week with fonts not showing up in Illustrator when activated in Extensis Connect. I'd have to restart Illy to have the activated font show up. Is this classified as a bug? Extensis support took me as far as they were willing to go then washed their hands of it and said it was an Adobe issue. Extensis plugin bug or latest version of Illustrator that doesn't work with Connect? I draw stuff, not develop software.

Link to the Adobe Community discussion that details the steps taken to get to a usable process:

https://community.adobe.com/t5/illustrator-discussions/extensis-connect-stopped-working-with-illustrator-photoshop-works-fine/m-p/15518093#M453965

The summary for the workaround was to uninstall 29.8.1 and revert to 28.7.10. Hopefully this gets fixed and both apps can cooperate again.