I think I priced Nominatim on EC2 and it came in around $350/mo because you need 64GB of RAM. Also on EC2 Pelias ended up being close to $100/mo. Keep in mind that I'm including EBS prices for around 500gb of storage for both of those. If you go with a bare metal server on hetzner (which most regular folks would do, and what we do for maps.earth) you can definitely come in under that.
Even if I'm off by a little bit or if EC2 prices are a bad benchmark, the fact remains that you need 100x less RAM to run Airmail than Nominatim, which felt novel enough to post about.