I'd stay away from TE with our 2nd round pick.
History shows you do not need to invest a 1st or a 2nd round pick to secure a good TE.
Travis Kelce (3rd round pick), George Kittle (5th round pick), Mark Andrews (3rd round pick), and Darren Waller (6th round pick) were not super early draft picks. Gronkowski was a 2nd round pick, but you have to go all the way back to 2010 for that. Vernon Davis immediately comes to mind as well, but he was drafted all the way back in 2006 (and how often do we want the Rams picking 6th overall?!).
When you do draft a TE early, it seems they are just as likely to disappoint for their draft slot as they are to live up to it. TJ Hockenson at 8th overall was a huge bust for that draft slot (although has had an okay career in absolute terms). OJ Howard at 19th overall was a huge bust. Kyle Pitts at 4th overall is also looking like a huge bust for that draft slot (but Atlanta is such a mess that it is hard to judge young Pitts just yet).
The highest pick I can recall working out at TE in recent years for giving fair value for his draft slot is David Njoku, who taken at the end of round 1. Ertz and Goedert would likely be the two main data points in favor of using a 2nd round pick on a TE. But as both were drafted by the Eagles in round 2, I am not confident reading into their draft selections as data points - more likely, IMO, is that Philly is simply good at scouting and developing the position.
So in short, it seems like a 3rd round pick is more than good enough to grab a good TE. And be it due to luck, the Rams not scouting and/or developing the position well, or the Rams' offense simply not maximizing TEs.... the Rams have been committing that level of draft resource to TE already without overwhelming success (although I do quite like Higbee).
Higbee was a 4th round pick, but he fell in the draft due to off-the-field concerns. He would have been a 3rd round pick otherwise. Coming out of college, many scouts had him ranked as the 2nd best TE in the draft class, behind Hunter Henry. He was unanimously regarded as a top 3 TE that year (some scouts had Austin Hooper ahead of him).
Gerald Everett was a relatively high 2nd round pick (44th overall). He was the 4th TE taken in that year, behind OJ Howard (bust), Evan Engram (seemed to be a big bust, taken in the 1st round / 23 overall, until a resurgence this year in Jacksonville, so time will tell), and David Njoku (very good player). Again, good-but-not-great.
The Rams also took Brycen Hopkins in round 4 in 2020. His career is still young but it does not appear he will be hugely impactful.
If this year's TE class is very strong, all the more reason we can wait on the position, IMO. Go elsewhere in round 2.