With your glutes you mean the actual gluteal muscles, not just surface pain from skin abrasion or pressure on your sitbones, right?
Pain in those muscles isn’t necessarily caused by your saddle. It’s more likely your overall seating position or a muscle weakness is the culprit. Even leg length difference could be a cause.
A sedentary lifestyle often leads to underdeveloped, underutilized gluteus muscles which can cause all kinds of issues from lower back pain to tightness/soreness of the muscles or Iliotibial band syndrome (pain on the outside of your knee).
The saddles which come with city bikes are often very wide and padded which is really only somewhat okay-ish with a very upright seating position. They look and feel comfortable at first but after a few minutes you realize that the saddle makes contact in all the wrong places.
I’d make sure that your seating position is okay-ish. Most importantly make sure the saddle is high enough. If you put your heel on the pedal your leg should be fully extended. Fore-aft position and handlebar position are harder to get right but also less critical.
All of those things are hard to assess without seeing you in person or at least having a few good photos of your on the bike.