It's entirely possible that GitLab could integrate Let's Encrypt and generate their own private keys. Some large shared hosting providers already do this (e.g. DreamHost).

Keys are cheap and plentiful, just regenerate & reissue however often you like. The paid CAs I've used do free reissues with new CSRs no problem. You are already trusting them to serve your site so adding a private TLS key isn't a big deal.

The only downside I could think of is if you are using HPKP with a long duration, you could have issues with rapidly changing keys. But I wouldn't expect GitLab Pages to support setting those headers so probably another non-issue.