Don't know anything about Drone CI, but it seems to me like a lot more work to manage two separate systems than it is to manage a single Gitlab instance, where everything is already nicely integrated.
I'm not a sysadmin by any stretch of the imagination, but I was still able to set up Gitlab, Gitlab CI with a bunch of runners, Gitlab Pages, and offsite backups with very little effort on my self-hosted instance. All I had to do was edit one config file to enable the various services (backups were with borg and systemd via the "gitlab-ctl" CLI)
Been running that setup for probably 2 years no with the only outages being external internet/power outages. I'm the only user, so my usage isn't at all going to reflect OP's needs, but it's still more reliability than I ever got from Gitea.