Yes, the ATF level needs to be measured with the engine ON, there are some you need the engine OFF like on certain years of Honda automatics. But many newer ones checked NOT fully warmed up (as in U760e without a dipstick), this is becoming the norm these days, not sure about which U-series transmission you have (sounds like the U151e?)
The felt filter needs to be periodically changed, and if plugged up, the clutch packs will wear out.
Not sure if yours is a torque converter issue or something else like dropped out of gear from pressure issues. I wouldn’t be looking at the engine or catalytic converters yet (did the dealer actually say that? Sheesh!) Did it feel like it was in neutral and then catches hard? Also could be wear debris caught in the valve body. For instance, the U660e was notorious for that as the case was too weak from bad design and The transmission slips just thousands of miles fresh out of the factory.
The link below is another member’s recent plugged filter and shift problems and an initial attempt to salvage with new ATF and filter. That was much worse at 165K miles, and looks like a rebuild in the picture there.
I personally would change the felt filter and ATF no later than 50K miles as in severe service if the vehicle's a keeper, earlier if using dino T-IV fluid (15~30k). I know, that’s a lot more than most, but I don't believe in the lifetime fill nonsense, as to me that's the 5 years/60K miles powertrain warranty period. Besides, parts and fluid are less than $50 if you DIY.
For now make sure the fluid is within range. Maybe the dealer is willing to reset the transmission memory for free.
https://www.toyotanation.com/threads/slipping-in-1st-hard-shift-to-2nd.1664547/
Dealers are usually clueless about transmission internals. I'd think they outsource that to the lowest bidder. They might have swapped a lot of torque converters in house to save a few bucks as those are problematic in various U-series transmissions. However, at 140K miles it's not bad. I personally don't have much respect for the U-series anyway. Just check out what 2018-19 Camry owners are dealing with the new 8-speed.
A $20 filter/gasket kit (rockauto) looks like:
https://www.rockauto.com/info/4/B-224_1__ra_p.jpg
Where in Texas are you, near Houston? If so definitely check out Circle D Transmissions. You can give them a call even if not nearby to see if they're willing to give you some advice.
https://www.circledtrans.com/
If not look up on ATRA, some can be duds, so check references.
https://www.atra.com/shopfinder