Looking at a house that has carpet in the living room.

It also has a wet underfloor heating system. I know very little about them.

I always thought carpet and under floor heating was very inefficient? Is this true?

Also, if I change to hardwood flooring, will I need to modify the system? Will it be a “carpet” type system?

You can have carpet as long as it’s low tog rated

We have wufh and have a mix of wooden and carpeted flooring. As massivespud mentioned, it depends on the tog rating of the carpet and underlay used, our is noticeably less plush, but still nice carpet to walk on.

As long as you and your thermostats/house heating system can sort out when to put the heating on it’s fine. Just remember that it’s not an instant heat by any stretch.
I can recommend the Honeywell Evohome thermostats and controllers as they cope well with our mixed rads and underfloor heating rooms without any fuss. It learns the heat profile of each room and turns the heating on at the right time to meet your ‘temperature at what time’ requirement. So if you were to change the flooring it would adjust accordingly.