No, time is not the same kind of dimension as space.
I think the thing here that confuses a lot of people is that we need to use movement over time to help our brains get some sort of grasp on how 4 spatial dimensions could work.
Think of it like how document scanners work: the scanner can only see a thin line, so to read the whole document it has to pass that line over the paper, which takes time.
On the other hand you have our eyes which can see a 2d plane, so we can see the entire paper at once, no time needed.
So the time needed to scan the paper isn’t part of the paper’s 2-dimensionality, but it’s needed to represent it in 1 dimension.
In the same way we couldn’t directly perceive things in 4d, but we could rotate a 4d item through our 3d slice until we’ve seen all angles of it, and then try to build a mental approximation of how it actually looks.
A concrete example: to map a 3d sphere into 2d, you’d move it through the 2d plane which results in it looking like a circle that appears out of nowhere, grows until it reaches the widest part, then shrinks again until it dissapears.
Similarily, a 4d hypersphere passing through our 3d space would look like a sphere that appears out of nowhere, grows and shrinks, and then disappears again.
Honestly it’s pretty funny to me how people think 4d is all strange and terrifying, when in fact it’s (to the degree that it can be said to actually exist, since it’s theoretical/mathematical) pretty “simple” and just headache inducing to try to wrap your head around.
like your mind wouldn’t shatter from being moved through 4d space, things would just look completely nonsensical and impossible, it’s no more lovecraftian than subatomic physics. It’s just Kronk saying “by all accounts, it doesn’t make sense”.