Brenbo, As above.
Get a good tar remover such as Autosmart Tardis or similar (there are a few good ones), your Auto Finesse one should be fine. Wash and dry the car the car then apply tar remover to the dry car, either spray on directly or apply with a very soft microfibre cloth a panel or two at a time, then wipe over very very gently with a MF (no abrasive action). Finally, rinse off thoroughly. Very important not to let the solvent dry on the car. As there’s so many tar spots you might have to repeat the process until the tar remover has dissolved as much of the embedded tar as it can.
Follow with the 'sandwich bag' test to see if there’s any tar contaminant left on the car - get a sandwich or freezer bag and slip your hand into it. Run you fingers inside the bag over the paintwork, panel by panel. The plastic bag will emphasise anything left on the car. If the paint feels glassy smooth then that means the tar remover has shifted all the tar. So just wash the car again and dry and apply some protectant. The key is to remove as much tar with the tar remover as possible leaving less to do at the abrasive claying stage.
If the sandwich bag test shows that there are still tar spots then you’ll need to clay the car using a clay bar and lubricant or a clay cloth or clay mitt, again with a dedicated clay lube or just a dilute shampoo solution to use as a lubricant. The claying process should pull off any remaining tar spots. Again afterwards, do the bag test.
All of this will remove any protection you have on the car (unless it’s a coating like Gtechniq Crystal Serum) so you’ll need to protect the paintwork with a sealant or wax.
Just as an aside, if you’re going to do all that, then you might want to give it a full decontamination and do the step of using iron remover (Iron X etc) after or before (doesn’t matter which) the tar removing but before the claying. This will remove any embedded brake dust and iron particles from the paint that build up over time and that normal washing cannot remove. Then you’ll have a fully decontaminated car.
Lots of effort but worth it to have the paint clear of everything. And well prepped to add a good level of protection. I’d do this next clear weather spell, or maybe even leave it till spring as your car will only pick up more stuff over winter, and of course the weather should be milder.