Can I make a leisure trip to California (vacation) in the current covid-19 situation as of 2021, will my quarantine be monitored?

My question is, can I take a leisure travel to california by Air out of state?

It's not illegal so you can.

I'm not sure what type of "leisure" you are looking for though. Pretty much everything is closed and in lockdown, so the most likely scenario would be being confined in a hotel room for a 10 day quarantine with take out food and no human contact. That's not my idea of a fun time.

Will my quarantine be mandated?

Yes

Since I will be travelling for few days, my trip would be useless if I had to quarentine myself.

Correct

What is sane advice that I should take?

DO NOT TRAVEL. This is a terrible idea in the middle of a pandemic spike with hundreds of people dying every day in California alone.

How much of risk I am putting myself and others in the current covid-19 situation?

This is a very high and completely unnecessary risk.

Rent an RV and drive it to the Carolina coast

Since OP's goal is to get some sun, I am proposing a closer destination on the US East Cost. I am not proposing to drive to California. "Carolina" is a pair of states a bit north of Florida.

It's a 13 hour drive. "Oh, that's so much longer than a flight" No it's not. I've crossed the country plenty of times. If you're honest about the "all-in" time from your driveway to the other driveway, it's about 13 hours from Boston to San Diego.

So "drive time" is a wash.

So what are the advantages of the RV?

• It totally eliminates a whole bunch of close contact other than sitting in the airplane proper... including queuing for baggage check, queueing for TSA security, waiting at the airport (which evidence is showing is a real problem), taking public transport within the airport site, waiting at the rental agency -- all places with no consequence for mask non-compliance, so off come the masks and you have a "super-spreader" event.
• It's wheels, directly, which means you can simply go from your driveway to wherever you want to go. The only place you have to stop is gas stations, and having recently crossed the country that way, this can be done contactless if you use a credit card to buy your gas.
• It's easier to roam and explore non-urban destinations, such as a remote beach or trailhead, since you're not forced to be near airports. Getting "out in the country" simply means less contact with people and gives you vastly better choice of safe activities. (and who's kidding who, they're on your bucket list anyway!)
• Carry your own food, so no restaurants. You provision your RV at the start of your trip. If anything comes up, simply do "curbside" at a big-box store where you're already set up. I did exactly that on my recent trip, and it was effortless and instant. (at Target, which really has their act together; this depends on using their app. Downside, Target stores are rare in Trumpland).
• Incremental cost for +1 person is nothin'. So take a partner or podmate.
• Or pet.

The only sensible way to tour California now during the covid19 shutdown is to do it virtually. Find videos that show the places you would visit and watch them instead of taking time money effort and risk to go their physically.