The setting is Earth, millions of years in our future. In this setting a species of tree has made an evolutionary leap, allowing it to bypass the water transport constraints currently thought to be the primary limiting factor for tree height in extant species. This leap occurred roughly in our 'present day', so this new species of tree has had millions of years to refine and perfect this newfound ability, as well as allowing it to spread to new niches where it hadn't previously been able to compete. Spreading to new places will allow it to eventually colonize areas where near-ideal conditions exist (weather, water availability, nutrient availability, etc.), allowing it take full advantage of its new height reaching abilities.
The exact nature of this evolutionary change are a subject for a separate question.
For trees (in many, though not necessarily all, environments), genetically taller individuals are often evolutionarily selected for, since height means more access to light. Given that the previous water transport height limit is no longer a factor, genetically taller individuals in this new species, which already had better reproductive chances than their shorter neighbors, will be able to outcompete their neighbors much more significantly. This will provide evolutionary pressure to drive the new species toward taller and taller individuals. However, the new species is otherwise composed of the same stuff as it's evolutionary ancestor (other than the newfangled water transport imrpovement). For the purposes of this question, the change does not improve, nor detract from, the structural integrity of the rest of the tree's composition, except as new height/weight/leverage and similar considerations are involved, the wood itself is otherwise unchanged in this regard.
With this new freedom to reach new heights, and the time to do it, how tall can a tree get?
Obviously, I don't believe that removing that one limiting factor will suddenly allow trees to grow arbitrarily tall. Surely they will encounter some new limitation.
I conceived of this question from a 'square cube law' and 'structural integrity of living wood' perspective. My guess is that the next limiting factor they encounter will be related to structural integrity of the living material of which they are made. This could include things such as compression strength to hold it's own weight, or flexibility vs rigidity issues to flex in the wind without breaking now that much longer leverages are involved, or related issues.
However, I accept the possibility that 'structural integrity' may not be the next limiting factor, and welcome answers that identify and use some other limiting factor I hadn't considered. In that light, please assume that any changes to climate, atmosphere, sunlight intensity, gravity, and other environmental factors that are certain to change over the course of millions of years, have a negligible effect on this species, at least regarding its ability to reach record heights. Let's not get bogged down in "what else might change in that time?", and stick with "this one thing changed, so what's the new result?"
This part of the EDIT is to address concerns regarding lack of focus on the question:
My original wording of the question included this:
"While not strictly required, I suspect best answers will be based on a species that is currently one of the tallest species (redwoods, yellow meranti, mountain ash, coast Douglas-fir, etc). How tall will this new species of tree be before it encounters that limiting factor, whatever it happens to be? (bonus points for identifying the next limiting factor)"
This led to concerns about failing to identify a specific species of tree in my question. However, the question is about what the new height limit would be for trees in general, which is why I intentionally didn't specify an origin species. The original water transport limitation applies to all current species, and whatever factor produces the new height limit should, in theory, also apply to all species (though, like the current water transport limit, relatively few species would challenge that limit). The list of already very tall species was based on my assumption that these species were already challenging the current limit, and so are among the most likely to push past it, given the opportunity, and challenge the new limit.
Whatever that new limiting factor might be, some species will have a head start, so to speak, in achieving new record heights, since they will already have better form factors or strength characteristics that will be particularly suited to going beyond their current heights. Unfortunately, I don't know which species that might be (included in my list or not). Limiting the question to a single origin species will not necessarily yield the answer to the question "How tall could 'trees' get? in this scenario, unless I accidentally (miraculously?) stumbled on to the species that is already best suited to it on my own.