I think Firefox Sync already restores your profile including add-ons, if you log into Firefox. Of course you may not want that for privacy reasons. In that case, I believe there is a way to self host a sync server, but I will have to go look for the repo for it.

Edit: https://github.com/mozilla-services/syncstorage-rs

Why not just keep /home on a separate partition? Or just backup ~/.mozilla/?

You can backup your .mozilla file from your home to a new install and it'll keep the everything how it was.

I've done it a few times now.

I know that some distros package Firefox extensions. Debian is one, here's one example: https://packages.debian.org/bullseye/webext-ublock-origin-firefox. So you could sudo apt install webext-ublock-origin-firefox

I install and use FF from my home folder. As a result, I can simply copy my 'old' firefox folder and .mozilla folder (containing the FF config files) into the new distro's home. That way all of the features, settings, and extensions remain the same, regardless of the distro I've moved to.

Inside the .mozilla/Firefox/ folder you'll find separate folders for your profiles. The 'about:profiles' window lets you switch between them.If you want to experiment with one, make an archive of its folder. If you try something that doesn't work out, you can throw the messed-up profile away and extract a fresh copy from your archive, all's well. There are also many files INSIDE that profile folder you can toy with. Many, many options in this setup.

I use something like this:

#!/bin/bash

set -euo pipefail
URLS=(
    'https://addons.mozilla.org/en-US/firefox/addon/ublock-origin/'
    'https://addons.mozilla.org/en-US/firefox/addon/privacy-badger17/'
    'https://addons.mozilla.org/en-US/firefox/addon/passff/'
    'https://addons.mozilla.org/en-US/firefox/addon/copy-plaintext/'
    'https://addons.mozilla.org/en-US/firefox/addon/duckduckgo-for-firefox/'
    'https://addons.mozilla.org/en-US/firefox/addon/user-agent-string-switcher/'
    'https://addons.mozilla.org/en-US/firefox/addon/clearurls/'
    'https://addons.mozilla.org/en-US/firefox/addon/temporary-containers/'
    'https://addons.mozilla.org/en-US/firefox/addon/consent-o-matic/'
)

DOWNLOAD_BASE_URL='https://addons.mozilla.org/firefox/downloads/latest'
_="${FIREFOX:=firefox}"
_="${DST:=/usr/lib/$FIREFOX/browser/extensions}"

if [ $UID -eq 0 ]; then
    SUDO=
else
    SUDO=sudo
fi


download_links=()
for url in "${URLS[@]}"; do
    package_name="$(sed 's_/$__' <<< "$url" | awk -F/ '{print $NF}')"
    download_links+=("$DOWNLOAD_BASE_URL/$package_name/addon-$package_name.xpi")
done

workdir="$(mktemp --directory)"
cd "$workdir"
for url in "${download_links[@]}"; do
    curl -OL "$url"
done

for ext in *.xpi; do
    ext_id="$(unzip -p "$ext" 'manifest.json' | jq -r '(if .browser_specific_settings then .browser_specific_settings else .applications end).gecko.id')"
    target="$DST/$ext_id.xpi"
    echo "$ext -> $target"
    $SUDO install -Dm644 "$ext" "$target"
done

That doesn't handle the extension config though.

Any particular reason you don’t just sign in? Genuine question, and you could even create a dummy account that solely holds those extensions and anything else you would want to sync.

You can use Nix with basically any Linux distribution. Here is my Librewolf config as an example: https://codeberg.org/jevans/nix-config/src/branch/main/homeManagerModules/gui-applications/firefox/default.nix

If you don't want to use Firefox sync, you can try just copying the whole profile folder from your backups.

i would say google is your friend: https://stackoverflow.com/a/37739112 without having tried it