Since it's Typescript, you obviously need to transpile to Javascript and host it somewhere you control for security (your own server is fine, just make sure the GPL license text is embedded). This is your GPL-respecting distribution of the software
Then in your webpage's index.html or other markup, include a `<script>` tag that links to it.
I believe this is all you need to be compliant with GPL.
[1]: https://unbiased-coder.com/can-you-use-gpl-in-closed-source/...
edit: much more detail in this answer: https://opensource.stackexchange.com/a/4385/10533
If there's any doubt, it seems like you'd be safe releasing a GPL-ed service worker which your website calls, as the boundary when calling a service worker is definitely enough for it to be deemed communication between two distinct pieces of software. This might be a bit difficult with a library that removes the background from your webcam though