Is there a LinkedIn integration?

There is a LinkedIn integration,

However it seems not-so-useful to me, because LinkedIn won't include people's LinkedIn profile URLs — instead, you'll get only the person's name, and email address.

So you won't know which person over at LinkedIn, has logged in.

Here're the docs: https://docs.microsoft.com/en-us/linkedin/shared/references/v2/profile#profile-fields-available-with-linkedin-partner-programs
They write:   "The following selection of profile fields are only available to applications that have applied and been approved for a LinkedIn Partner Program".
And that section includes Basic Profile fields with the person's LinkedIn "vanity name"   = the LinkedIn URL.
However the Lite Profile doesn't include the LinkedIn URL.

If you self host Talkyard, then you can create your own LinkedIn app over at the LinkedIn website, and contact LinkedIn and tell them why you want access to people's LinkedIn profiles / URLs, and try to partner with them.