Opinions needed please.

There's two EGR-related part numbers in your attachment:

1. 04004-58137 < From Google search, this appears to be just the EGR valve, perhaps with gaskets, to make it a "kit".

2. 25685-37010 < This is the gasket betwee the EGR cooler and exhaust manifold

For your info, the EGR cooler part number is 25601-37010, at least the original number.

I would suspect what they did was to remove the EGR valve/cooler assembly, replace the valve portion only, and also replaced the gasket between cooler and exhaust manifold. They may or may not have cleaned the EGR pipe. I doubt they cleaned the EGR cooler, just knowing how they operate. The intake manifold (with EGR passageways) probably also is untouched.

Assuming that was just recently, I think you better dive in.

Reference to @NutzAboutBolts videos, some threads, and info:

Nutz About Bolts Prius Maintenance Videos | PriusChat

Two or three other videos linked there too, for the full cleaning of the intake manifold, full EGR clean, and Oil Catch Can install.

Good thread:

EGR &amp; Intake Manifold Clean Results | PriusChat

Another:

Oil Catch Can, Eliminate that knock! | PriusChat

Some tools worth having:

E8 Torx socket (mandatory)
E6 Torx socket (optional, but good to have, to remove the throttle body studs from intake manifold)
3/8" ratchet wrench, regular and long handle, flex head, you can never have enough (or 1/2 plus reducer)
1/4" ratchet wrench, or 3/8" to 1/4" reducer
Ratchet extensions: you can never have enough
Long needle nose piers, straight and bent tip
Ratcheting 12mm box wrench (optional, but makes disconnection of the EGR cooler from exhaust easier)
Torque wrench (3/8" and 1/4" both good to have)
Floor jack and safety stands (or ramps): basically some method to raise front, if you need to take underpanel off, which you may need to, both for access and to recover dropped items.

 

Oh, and that was almost 7 years back.

Never mind, repair was 2017. Still...

 

While you're doing the intake manifold would be an opportune time to do an oil catch can install too. There's a link in my post above, a good Priuschat thread, and @NutzAboutBolts has a video on that as well.