Granted, there's no economical way you could self-host a Gittea instance to avoid this.
How are your git repos stored? Attached block storage? Seriously? Those aren't highly available at all, and it wouldn't even work in your proposed setup because each instance will have its own block storage.
No, that won't do. You'll have to implement some form of cross-region replication, possibly blocked by S3 or something. Good luck. Its not easy.
The only way I can think of accomplishing it is to make use of GCP's free f1.micro instance, so you can spin up two of those for pretty cheap in different regions ($3.88/mo). Have DNS hosted somewhere that can resolve to each of your two instances at random ($12/year? Lets's say $1/mo). Then you have instance storage; good luck finding globally redundant block storage for practically unlimited repositories, with backups, for $2.12/mo. Let's just leave network egress charges out of it, since those would be marginal.
And let's go ahead and say I value my free time at a conservative $30/hr. It takes me an hour to set this thing up and maintain it every year; horribly conservative. That's an additional $2.50/mo.
Maybe you can do it. It isn't laughably economical.
https://status.aws.amazon.com/
If there are network issues then it wont matter if you want to read or write to bitbucket