Former rower here: don't buy one without trying one. Also, if are bored by the stationary bike, I can guarantee you will be bored by the erg. Don't buy one.

A typical workout goes from 24 strokes per minute up to 34-36 strokes per minute in a sprint, so you are taking your strokes relatively slowly. The whole point is to explode with your legs and relax before the next powerful stroke. In order to row effectively, you need to learn proper technique and take it very slowly. You won't enjoy it. Competitive rowers don't even particularly enjoy the erg. It is either boring or excruciating, and either way it requires an amount of mental toughness that other cardio equipment does not. Every single stroke you take you have to commit to maintaining full power and explosiveness, or your speed drops. It is much, much harder to "zone out" on an erg than a stationary bike or treadmill.

It sounds like you just haven't found any exercise you enjoy and you are just hoping that if you spend money on a fancy piece of equipment it will solve all of your problems. I can promise you that it won't.

And as someone who used to row and even competed on the indoor rowing machine, don't get into rowing unless you really know that you will enjoy it.

That said, feel free to ask me any questions you have about other good forms of cardio or strength training. I know how hard it can be to find a good type of exercise and make it a habit. Since you're willing to spend some money, have you thought about buying a bike? Road cycling is a great social activity and groups are very welcoming. Mountain biking is just a lot of fun. You say you suffer from moderate anxiety. Does that stop you going out hiking, walking, or jogging? When I started running a bit as a teenager I always ran at night because I didn't want to be seen running. But you move past that sort of thing very quickly.