The trick is that land alone can command higher tax rates than land+buildings without negative economic effects, due to land having an inelastic supply. A community could therefore tax land value at ~100% and capture the entirety of the value increase that'd otherwise end up in landlords' bank accounts. Combine that with UBI or some other means to redistribute that captured value and literally the only “losers” in this scenario are the landlords (and only to the extent that they'd no longer make money on renting out land; slashing the building tax to zero would make those landlords less disincentivized to maintain and upgrade their buildings).

LVT would increase supply of rentable spaces by forcing landowners to utilize their land as the market demands.

So it directly solves for this problem by giving store owners more power in negotiations (I’ll just move across the street)

In the immediate order of things yeah, tenants aren't going to receive any relief from taxing land. The benefit lies in the second, or maybe even third order of effects that LVT produces.

Do we want the landlords to just sit on all of that value they're accumulating or do we want to take in more tax revenue (not a higher tax rate) as their land value increases and then do something for the common good with that additional tax revenue? Maybe tax relief for businesses, or social programs that reduce the cost of living for the workers. Or even better, encourage the landowner to further develop their land to get a better return, potentially benefitting tenants and the nearby community? Because that's what LVT does, or at the very least enables.

It does capture the increased value of the land around the shops though. Transferring that to the retailer is harder, as you say