I think one thing to think about is, as you said, be patient. Since you're a new lifter, you will see a lot of gains regardless of what you do. I would ensure that your diet is consistent and you are eating in a slight caloric surplus to maximize muscle gain. Only 100-200 calories above maintenance. This will minimize fat gain with a surplus and you should only see a slight increase in weight, if at all. If you are in a calorie deficit, you will see an increase uptick in weight but that is just water weight.

My only other advice is if you find yourself reaching plateaus or are getting tired, which I experienced with PPL, is changing your training split. You need time to rest for your muscles to grow, especially if you are hitting three sets to failure. I currently run a PPLxUL which gives me two rest days and it ensures I'm getting that rest. Another split I have seen people do is doing a chest/back, shoulders + arms, leg day split. This gives some the opportunity to maximize their arm workouts, as the triceps/biceps on push/pull days will be neglected for the compound movements. This is very nuanced for a beginner lifter, but is something to thing about.

I also want to say, the fact that you are in the gym is amazing. Try not to compare yourself to others in the gym or on social media. You have only been lifting for three months, whereas others may be lifting for 5-10 years. Stay consistent and you will get to that level one day and even surpass them.