Thinking this through, using my domain might actually be much less risky than using a host's. If Gitlab closes down, and someone else buys the domain, then I'm forced to make a massive refactor with little notice.

If I own the domain, I'm likely to continue to owning it until I shut down my company. At which point, no one is likely to be running my code.

Possibly different if I was developing an open source library or something, but either way there's risk and need to be thoughtful of the risk versus impact.