Like most indie puzzle games, the mechanics here are unique to the game. (I know this from watching the developer's updates as the game's mechanics evolved; I also have had one or two brief conversations directly with them during development.)
The questions you ask can't really be definitively answered until the game is out, but given the physical metaphor I'd suspect that the answer to the second is 'yes'. The first seems more unclear.
Update: Now that the game is out, it seems that the answer to both questions is "no". If a plant is ever pushed so that it has nowhere to go, it disappears - this is true whether it's pushed into a wall, another plant, or into the cactus's body. (Also, the game's good, go play it!)
Some of the updates over time:
In the original announcement, it's clear that the mechanics are the main thing being shown off. It's not directly stated that they're original, but there wouldn't be much to show if they weren't.
And here are some quotes from conversations about the game mechanics, as the game evolved over the course of the year. These are from a public Discord server focused on 'thinky puzzle games', where many indie game developers talk about puzzle design and occasionally give progress on their current projects. Even though the conversations are publicly accessible, I don't feel comfortable sharing too much of them, so I've kept the excerpts pretty brief:
5 May 2020:
[someone else]:
The 'growing plant' metaphor fits your mechanics so well. It actually clarifies so many parts of the game. It clarifies which end is growing, clarifies that its a rigid shape that can be pushed around. It gives you another feature to animate (flower pot), etc.
Mischka Kamener:
I know! I was so happy when I thought of it, but it took a while to get there. For a long time I was resigned to either go with a snake or abstract blob creature
25 Aug 2020:
Mischka Kamener: [...] the reason I went with having some gridlines embedded within the wall is to try to make it clearer where the grid goes into the wall. I think I've done that more in early levels than in later ones.
24 Sep 2020:
[someone else]: how's your cactus game? And yes, motivation is tough
Mischka Kamener: I did win an internal battle against scope creep recently though which I'm very happy about. I was thinking about adding in some other ideas, but ultimately they weren't as good as the core ideas I've already got [...]