Normally I'd have asked in the Comments for the specifics of what you'd used here as often knowing the exact products used is vital to diagnosing an issue, but I don't think it matters here as something else led to the uneven result you got.
So first off your tabletop is almost certainly oak as you thought. I only mention this as it's relevant to a few of the points that follow.
Panel material of this type made from many narrow strips will never yield a super-uniform result with conventional staining because there are so many different pieces of wood, each of which may be slightly (or very!) different to its immediate neighbours, and that includes how it absorbs stain. You can see this in a few locations on your tabletop, where one stave abuts another which is noticeably darker. This is normal and to be expected when staining conventionally.
That said, you can generally get a more even result than this; and there appear to be patches where the stain didn't take very well which I think give us the necessary clue.
What went wrong
I think the cause of the uneven colouring here is incomplete removal of the original finish. There are smaller indications of this here and there, but the top-left corner appears to be a patch where a noticeable amount of original finish remained.
Stripping is usually not a one-and-done thing. Pros often set out to strip twice, and may even be prepared to strip three times to ensure every trace of former finish is removed from the surface. This is especially important on open-pored or coarse-grained woods such as oak because finish can easily be retained in the deeper grain1.
On some species if you scrape or sand thoroughly and completely after stripping a second or third stripping may be made unnecessary, but with something like oak that means taking off quite a bit of wood because the grain is deep. This may remove more wood than you'd want to sacrifice if you can prevent it, although admittedly you do have plenty of thickness to play with here.
So, what now?
If you want to go very dark, like a dark-chocolate colour that's been popular for some years now, you may be able to leave what you have and apply another product on top to even up the colouring. That product is the poorly named "gel stain", which is actually a coloured varnish, artificially thickened to some level of gel consistency depending on the brand.
"Gel stain" isn't absorbed by wood but instead sits on top, so it is ideal for helping to achieve a uniform colour where absorbency varies. But, this comes at the expense of obscuring natural grain features in the wood (as all pigmented stains do).
If you don't want to go much darker however, the ideal course of action would be to strip again, ensuring this time that you are down to clean, bare wood2 and then stain again. Note that staining a large surface with waterbased stain can be tricky; you may want to look at a few guides to ensure you have all your ducks in a row before tackling this a second time.
Note on "wood conditioner"
Products sold as "wood conditioner" are intended to even up stain absorption in blotch-prone species, but oak is not one of those.
The blotch-prone woods for which these products (or some kind of DIY alternative) are intended include softwoods (chiefly pine), cherry, birch and maple. These are all poreless or small-pored/fine-grained woods. Open-pored woods, including oak and walnut, generally stain very nicely and without blotching.
Regardless of whether "wood conditioner" is called for or not one of the side effects of using it is that it automatically gives a lighter result. This is because it partially seals the entire surface of the wood, not just the problem areas it was applied to treat.
1 You can easily spot this after stripping, cleaning and sanding — shiny glints in an otherwise completely matt surface.
2 When you clean the stripped surface down with mineral spirits, lacquer thinner or water after stripping, use the opportunity to look for uneven wetting of the wood, which indicates areas of 'standout' where some trace of the original finish remains in the wood fibres. Only after the surface wets uniformly (no light patches that look like they aren't as wet) and there is no beading, are you ready to proceed.
