To answer this question, if you have Umbrel running Tailscale already, that’s most of the battle. Once you’ve got Tailscale installed, and your Bitcoin node is fully synchronized, then you can get started with BitAxe and public-pool.
Right now, documentation seems pretty sparse, but if followed, seems to work well enough. To run public-pool from your umbrel, install that add-on, and then in the settings for public-pool use “umbrel.local” as your TCP+Stratum user, Port Number: 2018, and then your Bitcoin node’s address (can be found from the Lightning Node add-on app on Umbrel by choosing ‘Deposit’ under the ‘Bitcoin Wallet’ section). You could use a different Bitcoin address for improved security, I’m just giving you the easiest “Getting Started” method for mining to your own node’s address.
Once this is done, make sure that your BitAxe has its settings changed to use the BTC address for your Umbrel. Remember that after updating BitAxe’s WiFi settings to use your own WiFi network it will get a new IP Address assigned by your router or DHCP server, so finding the AxeOS webpage is as simple as looking at the output on the BitAxe to see what it’s new IP address is. Enter that IP address in your web browser, and you will get the AxeOS webpage to load right up. After updating the BTC address on the AxeOS webpage, Save, and then restart the BitAxe.
Now, this doesn’t mean you’re earning sats just mining to your own pool – that only happens if you’re lucky enough with your pool of BitAxe rigs to hit on the solution that wins you 3.125BTC every ten minutes or so; you would need to mine directly to a centralized mining pool for the incremental sats benefits. But it does mean you’re adding proof of work to the greater Bitcoin community, and should other massive mining operations go down temporarily or permanently, we’ll all still be contributing to the open source, decentralized value of Bitcoin by continuing to find solutions and reaping the rewards. Also, our added hashing power makes it ever more difficult for a state government to usurp 51%+ of the total hashing power.