I would use hosting with SSH access. I am based in Poland so we have MyDevil.net
But also you can just rent VPS for 5$, but you have to care about setting everything up.
First thing I thought while reading was Firebase - it's interesting how much it would cost there.
hetzner cpx11 in Ashburn - 150 ms latencies to Europe are totally fine for this use case. with 15k groups and 162k expenses (guesstimating 30k users, email logs per-expense, etc.) , you're not even pushing 2 gigabytes of disk space (conservatively), nor are you doing anything computationally expensive or stressful for the DB under normal load. With decent app & db design, like proper indexing, 2 vCPUs and 2gb RAM is more than enough.
First thing I thought while reading was Firebase - it's interesting how much it would cost there.