Often1

This has nothing to do with Marriott, your corporate TA, or the TA's compliance software such as Concur. It has everything to do with the rates the TA's customer has chosen to use. That customer is not you. Rather, it is your employer and your beef is with your employer.

Your employer may have done this wittingly or unwittingly and it is often the latter. But, it may also have chosen to have the software limit travelers to lower rates which do not qualify. Essentially, the employer is not willing to subsidize lounge access and upgrades.

Bottom line is that you have a chat with your travel people to figure out why this is and whether it is fixable or whether you should e having a second chat. This time with a head hunter.

TBD

It would be unusual for a travel agency agreement to require the company to use booking.com or HRS content. But I suppose it's possible.

Talking to a headhunter because you don't like the points situation (likely a temporary issue) seems a bit overly dramatic.

C17PSGR

But quite possible for the company to have a travel policy that requires usage of the lowest rate, which might be a booking/expedia rate that doesn't earn points. The travel agency would then apply the policy directed by the company.

Marriott is, of course, pretty removed from that process.

TBD

That's more likely, yes.
Marriott is removed from the decision, but this puts significant pressure in Marriott to extend points to these fares. As I say above, the whole point of Marriott Rewards is for the hotel chain to influence corporate travelers.

Often1

That ticks off the large corporate accounts which expressly don't want to be in the business of subsidizing their employee's perks. Petty and short-sighted as it might be, there is a market for those rates.

Again, all comes back to the employer.