moving service entrance and upgrading to 400A with 200A workshop and 200A existing House panel

Yes you can bottom feed the old panel, I have even seen panels put in upside down to save 2’ of wire., it looks like you have a mix of breakers the inspector may hit you on that. I might start moving neutrals and grounds around ahead of time it looks like neutral on the right and ground on the left and having that done ahead of time may help with the inspector.

400A boxes

400A panels are expensive because nobody does that. The normal thing to do with a 400A meter is immediately split it to two 200A main panels, just ordinary common-as-dirt main panels, nothing fancy at all. In fact, ordinary/common "class 320" (read: 400A) meter pans provide for two 4/0-sized lugs per phase. That's not for paralleling: That's for splitting to two different main panels. You couldn't attach a single 400A panel if you wanted to, because the lugs won't take a 500 kcmil conductor, and they're not for paralleling.

For some reason, some people with a certain level of electrical knowledge get fixated on doing it some other way (sometimes they cannot believe you can just split to two main panels like that)... and they always wind up with an expensive adventure.

Now, given your requirements, what I would do is (gosh) split to two 200A main panels. One of the panels would have "Thru Lugs". The other would be the normal shop panel. So one-a these, and one-a these, coming off any common 320-class meter socket. Together under $300. You can spend a little more and get the better QO, Siemens, CH etc. I'm presuming outdoor for NEC 2020.

Anyway, feed the house off the panel with the thru-lugs. It's beholden to the 200A main breaker in that panel, so the run to the house is protected. It has 8 spaces for if you want to tap anything locally off that side of the service. The 30-space is for the workshop. I know it's smallish, but feel free to get a 40.

that was easy :)

The neutral bars (plural)

On your original panel, both sides are intended as neutral bars. They have several features that ground bars don't have. The panel provides enough neutral lugs for every space in the panel to be a "double-stuff" breaker feeding 2 independent circuits. You're nowhere near even half that, so you have the option to spin off one neutral bar to make it a ground bar.

However, that's not your only option. The common way to do that is to buy accessory ground bars for the panel ($8 or so). These bolt to the metal frame of the panel. You may find that more convenient if some neutrals or grounds are too short. You can get those (I would get 2), move the grounds to it at your leisure, and then simply remove the N-G boding screw or strap on Upgrade Day. I don't see one, which is a bit odd.

Routing the cables

Your proposal for cable routing (coming in the bottom when it came in the top/back before) seems perfectly fine to me. It's clear from your photo that the panel builder left you plenty of wire bending space for that purpose.

Make sure to put a knockout cover on any abandoned holes.

Penny-pinching now puts you in a bind later

There are two main problems with the setup you propose. First off, it relies on the rule of six as the meter-main you propose requires two separate breakers to be thrown to disconnect all the power; this is an issue because that rule is being curtailed in the 2020 NEC to prohibit a single panelboard enclosure from having more than one main disconnect. (Assuming TEP stands for Tucson Electric Power, then your power company's rules, as written, also require a single main disconnecting means.)

Furthermore, and more importantly, it limits you to only ever being able to provide 200A to the house, as NEC 225.30 says that you cannot have more than one feeder to a structure, and the exceptions don't apply to your situation by and large:

225.30 Number of Supplies. A building or other structure that is served by a branch circuit or feeder on the load side of a service disconnecting means shall be supplied by only one feeder or branch circuit unless permitted in 225.30(A) through (E). For the purpose of this section, a multiwire branch circuit shall be considered a single circuit.

Where a branch circuit or feeder originates in these additional buildings or other structures, only one feeder or branch circuit shall be permitted to supply power back to the original building or structure, unless permitted in 225.30(A) through (E).

As a result of this, you're much better off saving up a couple extra grand now for a single-disconnect 400A meter-loadcenter, such as the Siemens MC2442B1400SD(S), than backing yourself into a corner with a "rule of six" panel that won't let you expand the feeder to the house down the road. Imagine how frustrating it'd be to have a 400A service, but not be able to put in a Supercharger for your new Tesla because the feeder to the house can't go any higher than 200A.

Sizing the new conduit in keeping with that theme...

To keep with the theme of providing space for expansion, we will need to use a larger conduit from the new service location to the house. A 3" PVC conduit provides plenty of space, even for a 400A feeder (6x 250kcmil Al with a 2AWG bare copper ground, which takes up 1358mm2 of space, compared to the 1660mm2 available in a schedule 80 PVC conduit of that size); it will likely require a 3" to 2.5" reducer to fit your existing panel, but that's generally a tolerable state of affairs since going to 400A at the house would require you to add a tap box and a second 200A loadcenter, at a minimum.

As to routing the new feeder wires into the loadcenter...

You'll have to use the side gutters in your existing loadcenter for routing the new feeder wires from the bottom to the top, as your illustration depicts. However, both of the existing side bars in your current breaker box are neutrals, so you'll have to get an ECGB201/202 ground bar kit for your existing panel (presuming that it's a Siemens panel, that is) and fit it, then move the existing grounding wires to it.