That’s “creep mode”. The mode isn’t really all that smooth and in my experience causes a lot of shaking on its own (mine sounds like a rollercoaster climbing a lift hill), though a bad motor mount can make it much worse.
You can get one for cheap on eBay! Installation can either be DIY or any shop depending on the condition of the bolt holding it together. Though, that’s if you need it, you may just be feeling creep mode.
I made my own mount in 2014 using a sledgehammer and a bushing from a VW Golf control arm. I don’t recommend this route unless you have immense patience and/or more skill at destroying stuff than myself.
Also, I still owe you that muffler!

I should just take Friday off and get it done.