I'm not very confident with paper I like the metal way like crypto steel capsule. A bit expensive, but principle can easily be done with inexpensive materials.
If metal makes you feel safer, then by all means use a metal back up, but I don't think it is necessary. If you have your seed phrase backed up on paper in two separate locations as I said above, then many of the things metal protects against become irrelevant. Sure, a piece of metal will withstand fire, water, corrosion, etc., better than a piece of paper, but if you have a second copy somewhere else then it doesn't matter if one of your back ups is completely destroyed, since you can just recreate it from your second back up.
And yeah, there is no need to fork out $100 or more on a proprietary piece of metal; you can just buy a sheet of stainless steel for a couple of bucks from a local hardware store and do it yourself.
In plain simple: Having a physical HW wallet + knowing it's PIN will not give access to seed.
It depends on your model of hardware wallet. There are indeed some which will have the option to display the seed phrase to you again after the initial set up. This can be used to replace your seed phrase if it has been destroyed, but obviously if your seed phrase has been lost or there is any risk of it being compromised then you should move all the coins out of that wallet and to a new one.