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No, you're dealt 2 cards, not 13. You eventually draw 5 to 3 cards from the community cards

I mean in the sense that you can't change your hand.

Not exactly. You might think you have some control over your hand in hold 'em, but it's an illusion.

You get two private cards and five community cards. You can pick any five of the seven to use at the showdown. It feels like you get choice with the five-of-seven, but you don't really. There's always one strictly superior set (or trivial equivalencies), and that will be automatically chosen in any serious context ("cards speak".)

Draw poker does give you some control, by letting you discard some cards to get them replaced. There are also wackier poker variations that let you buy or pick or trade out more cards, but very little of that is seriously played anywhere.

I think you're agreeing with me. Holdem doesn't let you change your hand.

texas hold'em is a bidding game, not a card game, really.

Spade, you play some probabilities with your partner, so there is some skill in the card play itself, but not much. Especially in this common version with jokers and prescribed starts (big joker first).

In holdem you can fold or raise. If you fold you are obviously not playing your hand.