What's my best upgrade options

You didn't mention your room.  Every flat surface in your room is a transducer that reflects, cancels and muddies the sound.  How much does you sound change when you stand up?  How about when you lean forward in your listening chair?  Unless you have already treated your room I would suggest purchasing a couple of acoustic panels and just lean them up against wall and then move them and listen.

A simple heavy blanket over your flat screen increases clarity and depth.  If you have a coffee table between you and the speakers try moving and giving it a listen.  Acoustics don't have to be permanent but simple changes can make a difference and then can be removed for returning the space back to a more normal configuration.  You'll also learn what make a difference and when you want to make the changes for good you'll understand it better.

Agree with many that upgrade of the sources are a good next step. Also agree that going from rega P3 to P6 will not yield much benefit. I purchased a P10 last year and put it on the market the next day. My old Heybrrook TT2 with a Alphason HRS-100 MCS was overall better. There are very good turntables in that price point. Although, I prefer higher end belt drives, Technics looks very tough to beat in that price point matched with something like a Hana SL. The best cart under 1k$ IMHO. Good luck in your search.

Mainly in line with @goheelz if you have a lot of vinyl already then TT and perhaps phono stage, I have Origin Live (OL) decks and arms in ranges from £3k to over £25k and recently obtained (with a view to it being a starter for a friend) a Rega 3 with a (£500) Ania cartridge on it that they normally put on as the ’higher level’ choice over the Exact on the P6. Whilst it was ’ok’ put through a Whest Titan Pro II and Vitus Amplification. It could not anywhere near compete with either my putting a cheaper 2M blue on the cheapest of the OL decks and when I put the Ania cartridge on that it was better than the 2M blue and similar to a 2M black LVB. The Ania on that OL deck got more of the subtle detail that my MC Diamond pulls on the best deck.

So if Vinyl is your thing, I would move from Rega if you can audition an OL with a similar level of cartridge you have, especially it you could try it through a Whest Phono Stage it could give you an interesting comparison. Michael Fremer has periodically reviewed Origin Live from 2004 and the deck he reviewed then in Stereophile is still made now in a Mk5 version with cascaded learning as when OL launch a new flagship they cascade the learning to a new iteration of the ’old’ flagship keeping these competitive with some decks of 2-4 times the price.

Also a look at the testimonials on the Whest page may also encourage an audition of one of these even if you cannot try with OL. And I will note that with a Taiko Extreme Server and a dCS Vivaldi four box CD/SACD system. I go to the Vinyl almost exclusively and I re-built my vinyl collection after a 10 year break after I heard the Origin Live with a Whest Phono-stage. An OL Sovereign-S with a Conqueror or above arm and a Whest 40SE or above would be a very worthy Vinyl front end for your downstream system. For me the re-building has been worth it.  I also hear good things from those I trust of the Alphoson HR200-S Arm, but will likely not hear it until the Ascot UK show in a weeks time. 

But if you are not already heavily vested in Vinyl then I’d agree whether you go Qobuz/Tidal for less than 1 vinyl album a month you have ’the world’ of music. I have an Aurender W20 (not SE) and a Taiko Extreme, the latter is overall better the former is excellent as are several models in the range at their price point. dual aes/ebu Aurender’s like the W20 work very well with dCS Vivaldi DACS as they did design work together.
MSB may well be a preferable choice with a Taiko. But when I want them ’ in the room’ I still go with Vinyl, especially when there is a well mastered 45rpm version.

@OP As others have said, the system is completely unbalanced in terms of the source components versus the rest of it. If you listen to a lot of vinyl, the Rega 3 is the weakest component of all. Without breaking the bank, a Technics SL 1300G and, for example, a Hana ML cartridge would be a big improvement.

Also, have you listed to the system with the surge protector out of circuit? You don't say what make it is, but in general, inexpensive power conditioners are rarely an improvement.

Buy a very good Dac that is a big plus  cd player very limited  power cables too

your cables biggest weakest link ,having owned a Audio store for over a decadec

system synergies ,  for minimal cost Wireworld Eclipse speaker cables 

or platinum if you can afford  try to keep brand the same in interconnects cables 

a Litz cable preferred imo for no Cable Micro arching  worse only connect at the connectors .