In preparation for the swap, I have been able to sync my wallet up to block #375908 (last received block, indicated as generated two days before) but it was stuck there, with just one connection to the network.

Is this possible that the chain isn’t moving anymore, or that it has forked?

I tried to unlock the wallet and immediately started mining new blocks, but they don’t get more confirmations because it seems I am the only one staking.

What to do to solve this and be able to send transactions on the network?

What is the current block height on the right chain as of now?