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Every year/release this answer on installing previous versions of macOS will need updating. Last update May 2023.

TwoCanoes' MDS 'Deploy Stick' [free to use & open source, but without support or automation, which are paid add-ons].
This seems to be just about foolproof. A two-click solution.

Every year/release this answer on installing previous versions of macOS will need updating. Last update Nov 2023.

TwoCanoes' MDS 'Deploy Stick' [free to use & open source, but without support or automation, which are paid add-ons].
This seems to be just about foolproof. A two-click solution.
Update Nov '23 - Since V5, MDS now seems to be paid only. Try v4.3 or older from https://twocanoes.com/products/mac/mds/history/ & report back in comments if that still woks as freeware.

TwoCanoes' MDS solution 'Deploy Stick' [free to use & open source, but without support or automation, which are paid add-ons].

Mist from ninxsoft which can download & build official installers.

TwoCanoes' MDS 'Deploy Stick' [free to use & open source, but without support or automation, which are paid add-ons].
This seems to be just about foolproof. A two-click solution.

Mist from ninxsoft which can download & build official installers.
MDS actually uses this as its download mechanism. This is the more 'raw' version, but also looks more powerful if you need additional tools.

First see MDS or Mist, above, if you have access to another Mac.

Always use Safari when trying to connect with anything to do with the Apple KB or the App Store.