How big is a Bitcoin transaction anyway?

Bitcoin block 841,308 (most recent as I'm writing this) is 1,615,771 bytes and has 3,148 transactions, for an average transaction size of ~513 bytes.

Because a Monero transaction is about one and a half to two kilobytes

So yeah, about 3 to 4 times as large as an average Bitcoin transaction.

Keep in mind we have dynamic block scaling so that the blocks will get larger as more transactions come in.

That's not a scaling solution, though. Larger blocks provide throughput at the expense of decentralization, since fewer people will run full nodes as resource usage increases. Eventually it gets to the point where it becomes feasible for a government to track down and compromise all the remaining node operators.

It seems like lightning service providers may very well be considered money transmitters

Not sure how much this would matter. Lightning wallets don't care whether their channel partners are registered money transmitters, or just some rando operating through TOR or in a permissive jurisdiction. In the case of Samourai, taking down the backend rendered the wallet useless. Taking out a lightning node just temporarily inconveniences users that were connected to them.