Hi,
Both of my cats were diagnosed with heart murmurs due to left ventricular hypertrophy. When Cat 1 was diagnosed both of them were young (under 1 year) and we didn't have insurance. We immediately got insurance for both (Cat 1's obv didn't cover her for any heart stuff) and within 3 months Cat 2 was also diagnosed - but fortunately she was covered.
Both our cats saw a kitty cardiologist (I didn't realise this was a thing either) regularly. Initially every 6 months and then tapering down to every year because they were stable.
The assessment took about half a day each time. Cat 1 was always a bit skittish and so usually needed some sort of sedation. Our cardiologist used a range of drugs, always trying to use the least amount possible, and something that wouldn't affect her too badly. But once he had to use ketamine!
For Cat 1, who wasn't insured, the assessments cost £600-700 each. The cardiologist came to our local vet surgery and did a full check up including sonography and he would record the scans so when I came to pick them up he would talk me through the findings as we watched the video and share the full set of notes. If they weren't too skittish (they were usually pretty calm with him) he would whip out the double ended stethoscope and let me listen to the murmur, explaining what I was hearing.
He put both of them on aspirin, which needed to be crushed and mixed into food twice a week. This was not expensive.
We had 5 really good years with Cat 1 where she didn't seem at all affected by the heart condition, before she very suddenly had a blood clot (saddle thrombus) in the middle of the night. It must have been very painful because I had never her her cry like that before. We immediately took her to the vet hospital where they examined her and eventually explained that her chances of survival weren't great and even if she did, she would never have the use of her back two legs again, and would be at risk of another clot. So we had to make the very sad decision to let her go.
Cat 2 however, is still going strong at 14 years old. Her condition has not changed all (i.e. no deterioration, no worsening of the murmur) and seems well managed with just the aspirin.
Having a good veterinary cardiologist made a difference. Ours is called Craig Venter. I think he travels all over the UK doing clinics. I couldn't rate him highly enough.
I hope this is helpful.