Can an independent clause be interrupted by a conjunction without a comma and still be an independent clause? [closed]

Can an independent clause be interrupted by a conjunction without a comma and still be an independent clause? e.g.:

He poured me another drink and I drank it.
or:
Max climbed onto his horse and we rode away.

Would these be considered compound sentences? Or are these sentences grammatically incorrect?

As far as I know, compound sentences must include a comma. Is this information incorrect?

Yes, that is a compound sentence. A clause has a subject and a verb, and can stand on its own, and since both clauses can stand by themselves, they are both independent clauses.

https://grammar.yourdictionary.com/grammar-rules-and-tips/independent-and-dependent-clauses.html states the differences between independent and dependent clauses.