How to recognise GitLab remote by HTTP header?

Problem to solve

I'm working on GitLab support for git-credential-manager [since implemented, see GitLab docs]. This makes it easy to conveniently authenticate to HTTPS remotes in web browser (OAuth) without having to create a personal access token.

Select an authentication method for 'https://gitlab.com/':
  1. Web browser (default)
  2. Personal access token
  3. Username/password
option (enter for default):

A problem is identifying GitLab remotes. A heuristic is "domain starts with gitlab.", but this isn't the case for many GitLab instances, such as https://salsa.debian.org/ and https://code.videolan.org/ (more examples). It would be neat to recognise a GitLab remote by some HTTP header. Then git-credential-manager can offer help with OAuth.

This is how git-credential-manager recognises enterprise GitHub instances, by looking for HTTP header X-GitHub-Request-Id.

Proposal

Include some kind of X-Gitlab header on GitLab HTTP remotes:

Current headers from http -h head https://code.videolan.org/videolan/vlc.git

HTTP/1.1 302 Found
Cache-Control: no-cache
Connection: keep-alive
Content-Type: text/html; charset=utf-8
Date: Sat, 01 Jan 2022 17:23:16 GMT
Location: https://code.videolan.org/videolan/vlc
Pragma: no-cache
Referrer-Policy: strict-origin-when-cross-origin
Server: nginx/1.21.5
X-Content-Type-Options: nosniff
X-Download-Options: noopen
X-Frame-Options: DENY
X-I-Am-Here: foo
X-Permitted-Cross-Domain-Policies: none
X-Request-Id: 01FRBANG0QMQX9XGTWN9HWDF2X
X-Runtime: 0.034397
X-Ua-Compatible: IE=edge
X-Xss-Protection: 1; mode=block