When I first started cycling I could easily reach 165bpm without ever getting muscle burns. But it seems now it's the opposite. I can maintain the same speed as before at much lower heart rates while my muscles start to burn early which makes it harder to reach the high heart rates that I used to. What does this mean? Is this normal? Is this a sign of progress of my heart?
Normal signs of progress. If you rest a few days, you'll see your HRs go back up. OTOH, you can also work on getting your legs stronger and more resistant to hard work. During the season, I'll usually leave it about like you have it. HR doesn't come up easily, though it will come up with hard effort. Getting in lots of vertical to get the legs strong. Then tapering a bit or taking a few days off when I want to have more fun/stronger performance.