Wanted to gauge what the issue(s) might be with my engine

How recently did you get it, and at what miles?

I'd suspect head gasket failure, judging miles, 3rd gen reputation (including the v's) and the codes you've got.

For the oil loss, check if you've got the "low-tension" piston rings, compare your VIN to the attached. For that, you can either replace pistons/rings, or new short block.

 

Almost certain to have a head gasket leak and excessive oil burning which led to the cat failure.

If you want to keep it and the rest of the car is excellent, get a rebuilt engine.

 

At 330K miles, replaced the cat last year, was a taxi before you got it, 8 trouble codes, V shutdown and wouldn't run currently, burns oil more than typical ( how often do you add oil and how much oil a week? )
Anything else you noticed ?
From a repair / diagnosis cost basis, and the fact your mechanic is recommending an intake manifold to start you off, you might want to check how much for a engine swap, before you go for the manifold while keeping your fingers crossed the cars not gonna need another repair after that.
Or contact Hybrid Pit Stop or Gasket Masters and ask them how much for an engine install, if they are close enough to you.
Gasket Masters ( main location in the bay area ) does a lot of work on taxi s so might be able to give you a better idea of what is wrong, listing the things you've already posted.

 

Your codes are: (1–4) a lot of misfiring; (5) the mixture too lean, a perfectly cromulent reason for a lot of misfiring; (6) the ECM not trusting the airflow reading, hand-in-hand with the mixture too lean; (7) the cat issue you already knew about, and (8) the engine producing piddly power, no surprise with the too-lean mixture and all that misfiring.

A hole in the intake manifold lets air in downstream of the flow sensor, which makes the mixture too lean and the flow reading not trustworthy, so yeah, that can be the whole story except for the oil consumption and the cat. Fix the hole before jumping to any other conclusions about the engine.

The oil consumption is still going to be a nuisance, though, and no good for a replacement cat.

 

It’d be interesting to know in more detail the nature of the intake manifold hole. It might be an extensive crack, but if small maybe 2 part epoxy would fix.

 

Get a new engine.

 

If an engine swap is worth the cost calculation of a Prius with 330K miles.
Or go with the mechanics recommendation, while knowing you're rolling the dice with repair costs, either way.

 

I also agree with this.... but out of oil weekly sounds pretty bad.
But coming up....
Brake Master
Traction battery.... water pump unless it's been changed..... and what about the AC....

 

I had to go back to the OP and make sure the out of oil in a week was the actual wording in the post, because I missed that exact wording in with all the other issues listed.
Seeing that is exactly what is posted in the OP, I'm not sure I'd even go for the new engine on a cost to possible future repair(s). But that's just me and I've got my own money pit sittin on a 12 volt tender waiting for a deal.

 

When Toyota did free rebuilds to replace the pistons and rings on these cars it was because of excessive oil consumption like the op’s car. The kind where you often run out of four quarts and get that pesky oil pressure light. A rebuilt engine is the only way to save a 300,000 plus car with terminal oil consumption. Especially after replacing the clogged cat. Who cares about the fuel trim or egr cleaning at that point.

 

Well, if the rebuilt engine doesn't come with an intake manifold and this leaky one is reused, the fuel trim is gonna stop that engine from running too.