(This post was not supposed to get too long, but you know me. Blah blah blah.)
I'm kind of surprised by that. So, it's okay to play golf with 3 other people out on the course, but not okay to putt solo on the practice green? How is one more dangerous than the other? As long as there are no pins to remove and replace on the practice green, I see no more threat than actually playing golf in a group for four-plus hours. Being outdoors and mostly socially-distanced by inherent design, neither seems too risky.
I'm all for caution, but some Covid-related restrictions make no sense when you see something else far more unsafe that is allowed.
In any case...
...you can practice putting on any lower pile carpet in your home. I do it every day as part of my regular routine, along with chipping off a mid-pile carpet and yoga stretches. It's like brushing your teeth. It's just another part of your daily maintenance process. Sure, it won't help you read breaks better, but it will certainly help you find and ingrain a good stroke and give you confidence that you can hit the ball on the exact line you want, every time. It will make you a much better short putter.
I cut a 4 and a quarter inch hole in a piece of thin veneer (1/64th") that is about 5 inches square which I throw down on the carpet as my target. (Card stock would work as well.) Or, just put two tees 4+ inches apart. Or multiple pairs of them along a 3, 6, 9 or 12 ft. putt line and practice sending the ball through all pairs and stopping just after the final pair. I use the same veneer framed hole for my chipping practice.
My general habit is to chip about 25 from different distances (I have about a 40' area in my finished basement where I can do this), then do my yoga, shoulder and back stretches, then chip another 25, putt 25, then head to the course to practice and play for real. It just re-affirms my confidence in my stroke, knowing I can make a smooth motion and perfect strike nearly every time.
Also, I'm not sure if you have a lawn, but if so, practicing your chipping and pitching from every conceivable poor lie out there will really help you see and find what works and what doesn't. I can spend hours each week, with one or another particular wedge and a dozen balls chipping and pitching to targets all over my backyard, simulating the kind of tough lies you might get on the course. I can't tell you how helpful this has been to my short game. Practicing at the course in a short game area is good, but in my yard with the difficult lies I can easily find myself in, takes it to the next level.
And just one tip to remember for mostly all chip and pitch shots, hit down on the back of the ball. Ball first contact. Just like any other full iron or wedge shot. No flipping. Only a flop shot and a bunker shot would not necessarily follow that standard.
Okay, I'm done.