1. Bot prevention. If the bots don't know that you're doing this, you might have a reliable bot detector for a while. The bots will quite possibly have no extensions at all, or even better specific exact combination they always use. Noticing bots means you can block them from scraping your site or spamming your users. If you wanna be very fancy, you could provide fake data or quietly ignore the stuff they create on the site.
2. Spamming/misuse evasion. Imagine an extension called "Send Messages to everybody with a given job role at this company." LinkedIn would prefer not to allow that, probably because they'd want to sell that feature.
3. User tracking.
Wonder if with things like Moltbot taking the scene, a form of “undetectable LinkedIn automation” will start to manifest. At some point they won’t be able to distinguish between a chronically online seller adding 100 people per day with personalized messages, or an AI doing it with the same mannerisms.
[1] https://business.linkedin.com/sales-solutions/social-selling...
I imagine most users will also not have extensions at all, so this would not be a reliable metric to track bots. Maybe it might be hard to imagine for someone whose first thing to do after installing a web browser is to install some extensions that they absolutely can't live without (ublock origin, privacy badger, dark mode reader, noscript, vimium c, whatever). But I imagine the majority of casual users do not install any extensions or even know of its existence (Maybe besides some people using something like Grammarly, or Honey, since they aggressively advertise on Youtube).
I do agree with the rest of your reasons though, like if bots used a specific exact combinations of extensions, or if there was an extension specifically for linkedin scraping/automation they want to detect, and of course, user tracking.
(except they won't, because they're not after money but engagement, and their built-in tools suck on purpose to maximize wasted time)
I would guess this is for rate limiting and abuse detection.