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Hydrant shouldn't be an issue and all that foliage tells me that there is no existing concrete to worry about. Should be an easy job once you have dug out the garden.
You might have enough space to keep a green border so not all the plants would need to go. The contractor will advise on permeability as anything you do will need to comply with suds regs. The council will probably want the drive done and to be shown a suds cert before they do the dropped kerb and lower the hydrant.
Our neighbour just had theirs done, took the council a couple of months to come and do the kerb after the drive was done so don't get your hopes up for a quick job. You'll likely have a lovely drive to look at for weeks before you can actually use it.
Do you have a dropped kerb already? 2k to the council for that bit.
Gravel 2-3k
Block pave 3-5k
Resin crap 8k+
Lifespan longest to shortest: gravel (with top ups) then block pave (with maintenance) then resin crap.
To clean, buy swimming pool chlorine, water down to a 4:1 water to chlorine solution, fuck nature and all fish down stream of you. Weeds are gone.