Ok, I found something. This is not the problem @DaveK was having though.
They are indeed rate-limited, but Logster rate-limits them even further, at one per minute per IP, resulting in 429 errors when there are multiple deprecation warnings in a single page load.
This actually causes deprecation warnings to get lost, making the /logs less valuable as a tool to find all deprecations…
a 1 minute rate limit to all JS error reporting per IP
https://github.com/discourse/discourse/commit/8db38de9d7d47b8c931ae0cc409c5550e37653b7#