One of the things I don't like about Dungeons and Dragons - any edition really - is that it is really easy to lose the sense of scale for the world. Your PCs are a group of 4-6 people who go around, crawl into dungeons, and come out bristling with magic items and weighed down with money. That's fine. You can have an idea of wealth.
What you lose though is just how ridiculously strong they are compared to normal people.
There's a reason most games end by level 15, and I think part of that is that after level 10 you start running out of realistic things to challenge the PCs. At level 10 a single PC should be challenged but is expected to win and be able to keep fighting: a banshee, an elephant, or a wereboar. So we're 'halfway' through the level curve and we're already at things you don't tend to find lots of those running around. Also at level 10, even with the action economy being against them, that 1 PC should be able to take out 12 or more 'guards', 'bandits', or 'soldiers.' Or - last comparison, I swear - 1 level 10 PC should be able to take two polar bears in a fight and only have it be a medium encounter.
But scale is important. It can break story immersion when every encounter your PCs come across is perfectly balanced for them with 3-5 monsters or less. Knowing that your 'average city guard' is CR 1/8 and keeping to that is also important for your world, and lets you do encounters that narratively make sense - but mechanically might be broken.
More importantly though, maintaining your sense of scale - and using your sense of scale - will be the clear sign to your players that they've grown in power.
Consider the following: Your PCs start adventuring and run into a town where the guards are a tough fight. Then they go adventuring and have a tough fight with some goblins. Then they go back to town and have a tough fight with the guards (even if this group is a different, stronger group). Then they go adventuring and have more tough fights against bigger monsters. Come back to town, and the next group of town guard they're running into is still a challenge.
Yes, they're growing. They're going up in level. But the world is leveling with them so they never feel stronger. Yes, they're going from goblins to dragons. But every time they fight it is a harsh challenge. They never get to feel strong. They never get to feel like they're a big deal.
Now compare that with the PCs start adventuring and have a rough start where they lose a fight to the town guard (a squad of 12-15 we'll say.) They get out, go on an adventure, beat up some goblins and come back. They want revenge. They fight those guards..now it is closer to an even fight. They don't win, but they don't get arrested either and flee before more guards arrive. They level up even more. Save the king, do that adventurer stuff. Come back and now they can beat those 12-15 guards.
See the difference? They have that bar. They can see their growth. They're at a point where 12-15 city guard aren't a "problem" so much as just something they can deal with. And if the world reacts to that - that these guys can take out multiple squads of normal soldiers no sweat - they'll really feel that growth. This will also make those enemies who can challenge them stand out. The baseline isn't "everything is a tough fight." The baseline is "we're stronger than most, these people are a challenge for us, therefore they must also be strong."
Remember scale. Use it. Let it color some of your encounters. If they run into a squad of soldiers, drop 20 soldiers down and see what they do.