I will add some learnings as I have been building mine this past few months...
When I designed mine I ended up leveling out a berm all the way around that was slightly above the pond edge. I tucked the liner under it. So it served as a physical barrier to keep the muddy water out and keep the pond liner tucked away.
That helped a lot. But as others mention, with the heavier rains, I found some areas would fill up outside of that berm but have travel getting rid of the water fast enough which caused it to flow back into the pond, over that small berm. Building a bigger berm probably would have solved that but the issue was only in 2 areas which were very close to each other. This would cause the pond to get extremely dirty.
I have almost full clay and it would dirty up bad. I couldn't see past an inch or two. Mine though, would clear up within a few days. Mostly settling to the bottom (or filter).
Since it was just the two areas that were very close to each other, I ended up putting in a catch basin (with atrium style top since I'll be adding mulch and landscape to these areas later) which is at the lowest point near my problem area. I moved a little dirt and created a small divot to help bring water from other parts to this same part. That and as time goes on, rain will wear away some of the dirt and find it's way to this catch basin. So it should only get better and more water from areas get into this drain. I trenched some 4" drain pipe out to my dry creek bed that runs at the back of the property to a real creek. I spent time in the shed every time it ran to see how it all flowed and just a few more tweaks to make sure it all goes to that catch basin.
This catch basin at the lower spot has taken care of all my issues (as of right now). Even some of the other areas will run back to this catch basin to get all that water out. So far it has handled well. Every time I make any changes as I finish up the landscaping, I go out when it rains to just verify. You never know for sure what is happening unless you see it happening real time. But do not wear flip flops... I've had them get stuck in the clay many times. Always fun...
Trenching that 4" pipe was some work though. One other option if it is a big issue for you is put in some sort of sump pit. You can get a sump pump and push that water out somewhere without running the larger pipe. You can run a garden hose or poly pipe. It will be easier to trench and even possibly just lay the house on top, hidden by rocks (or something else). Just keep in mind winter and freezing if that becomes and issue for you.
I've done something similar with the sump pit. My gutters for garage and house run down into 4" pipe that runs across my yard to the creek. Unfortunately, when planning out my pond, this area is lower then my pond. So I couldn't naturally feed that rain water back into my pond to refill. Pond was put in to hold water for irrigation in my yard (FYI). I ended up putting in a sump pit in. I run the 4" pipe that went to the creek into the sump pit. I have an over flow 4" pipe put in that goes back to the creek 'JUST IN CASE' the pump I have in there can not handle it.
I bought a 12V DC pump with float/auto shut off and placed it at the bottom. I wanted DC for the safety of it. I ran landscaping wire with my other landscaping wire over to the pump. I bought a DC power converter and basically feed that pump 24/7. So as rain travels down to the piping and eventually drains into this pit, the pump kicks on / off and fills my pond. I have a simple check valve in place too. But it has worked wonderfully.
So technically, you could do something similar but instead of pumping 'to your pond', you would just push away from your pond. No different then what a real sump pump in the house does. I can get you the exact list of things you would need to go this route if interested. But it would cost some money. Probably $100-$120?
But I understand the clear water. It bothered me so much to have the dirty water after a rain. I spent some time getting it cleared up but really, catch basin to move water away from the pond naturally really helped. But I could see the sump pit / DC pump idea would work just as well, if you can't naturally let the water flow away (or do not want to trench a 4" line away).
Ignore the mess in the pictures. I'm still in the process of finishing up landscaping and cleaning up the edges. It has been ongoing work. Still lots of rocks and plants to place. I'm also finishing up the grading where the sump pit is. I just put that new pit in a few weeks back.
(CATCH BASIN)
(SUMP PIT W/ 12V DC PUMP TO PUSH WATER UP TO POND)
(FEED TO POND FROM 12V DC PUMP)