Not in any order tips - and I completely agree with the NEVER to use standby option. It messes up with WiFi connections too when switched back on.
Buy an external hard drive if you don't already - you store all your PS4 games on that and leave the few PS5 games you play on the internal. I'm not even looking at the SSD ones they will be compatible with soon as the prices are ridiculous. Unfortunately the internal storage is still far too small for days like these.
Search the store for free PS5 upgrades - Mainly, the only way to see if a game you own and is installed as a free upgrade is via the store. Games like Destiny 2, Rainbow 6 and Valhalla have free upgrades - the full current list is here >> PS5 upgrades. The upgrades help visually but I think they are way worth it more for loading times more than anything else. Oh, and the Haptic Feedback in the controller too if it has that upgrade included!
Recording voice chat for everyone - theres more places annoyingly you can mute yourself by accident on recordings or just in chat. Be careful on the controller as the small button that mutes your voice is easily pressed and superceds your own mic mute. Check settings to ensure voice is shared and also check when in a party that your voice is set to Always Allow on sharing. We miss so many funny moments cos we can't hear everyones voices.
Saving screenshots and videos is now a couple of clicks - its very slick but a subtle change is being quick with the share button on teh controller and selecting then what you want to do. You can on teh fly save a 'quick video' and it offers to save last 30 seconds, 5 mins, 15 mins and so on rather than the last video which is as standard set to 60 mins.
Favourite all your 'parties' - Especially all the FG ones! The friends screen defaults to parties and its quicker to see if someone is on mic in one. You can also now slice and dice what you mute....hence now no need to leave a party if you find people are sending messages into a huge party that has loads of us in!
Inviting/Join people to games is done via party menu - Press PS button brings up the card view. You can then press on the names and invite to game straight via that way - and joinign can be quick that way too.
Auto updates to games works better....for recent games - All the games you've recently played (left to right on the main menu) should auto check for updates every time you turn on the PS5. If you need a game updated from your library that has dropped off the recent list, i'd always suggest clicking Options and checking for Game Updates. Better than PS4 but sometimes can be a pain still but thats the world we live in now.
Checking you open the right Game version - If you have the PS4 and PS5 version installed, before you start the game, press the Option button and 'Check Game Version'. Whichever is ticked will be the default one that opens for you every time.
Some upgrades don't need teh disc to be in anymore! - Destiny 2 and Wreckfest PS5 versions don't need the disc to be in which is pretty decent tbh!
If theres more i'll come back and share!