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lack of transactions in a block does not make it invalid, the miner may choose not to add any transactions (except the Coinbase transaction which states where the rewards should go to), however, most often than not, this isn't done with the intention of not wanting to add transactions, miners will start working on the next block right after a block is found, it takes a bit of time to deal with their mempool as they need to download the previous block's transaction list and remove all those transactions that were included in that block (failing to do so the block will be invalid).

So while downloading and working on the transactions, miners will start trying, if someone manages to hit a block before including any transactions, they will not hesitate to propagate the block, and that's how you see empty blocks.
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What you're proposing is basically a normal pool. You can of course connect to one of them, there are plenty. But this one is different.

In normal pools everyone contributes their hashrates as a group, and it doesn't matter who finds the block, the reward is divided proportional to the hashrate you provided. That way you get a constant payout every day/week/month, but the payout is much smaller. There are other variations of how the reward is divided in some pools but the main idea is the same.

Now, in solo ck pool you get paid zero until you hit a block(which might never happen), in which case you get the reward plus transactions fees, minus a pool fee. The chances of finding a block solo are really small though, but the payout is much higher. Plus, it's something unique to mine your own block.

Of course everyone has different preferences, and you can try many pools for as much as you want and keep changing until you settle in whatever you want. You can even rent your hash rate in nicehash so that other people can find blocks with your miner and you get a constant payout. Some people in this forum rent a lot of hash rate from there and have found many blocks, using ck solo pool.

Asic miners will blow away any current GPU when mining BTC or really any SHA256 coin.

The GekkoScience Compaq F is pretty powerful for being an USB stick however.... The reality is that it's extremly low power when compared to something like the Bitmain S19.

On a personal note your 3090 would be best served mining ETH.

The point is buy an Asic for mining BTC