Update: As of 2021, NY Metlife stadium is the only field without a midfield team logo. Carolina now has a panther midfield and LA/SoFi is applying logos for both teams.
Those are the only two.
The two mentioned, plus L.A. Coliseum as currently used by the Rams.
The end zones at Metlife can be (somewhat) easily removed so the team logo for the playing team is displayed. But the time and effort to do the same on the center is prohibitive.
For the Panthers, it was apparently such a big deal for Carolina to get the franchise that the owner Jerry Richardson put it there as a way of thanking the NFL. The placement of the shield seems to be his personal decision. In an ESPN Story, he's quoted:
We have the NFL logo on the 50-yard line for reasons we have talked
about before -- we want to reemphasize to our fans that this is NFL
football and not something else
The sources I used probably predated the Rams move to L.A. and did not mention their current (2017) usage of the L.A. Coliseum. I missed that one and as GB11 points out, there's no team logo there.
As the new Los Angeles stadium is also planned to be used by two teams. We'll have to wait for the opening to see if it will be similar to Metlife or if they have something else in mind.
2021 update. I wasn't able to find any discussion of the technology used, but so far they are repainting the logo for both teams. The chargers game had a Chargers bolt logo, and the Rams games have had two different Rams logos.