My tank is roughly 6.5 the city water looks closer to 6.8 or 7
faucet ph and my Established tank ph differ slightly
Hello; First from what I read tap water pH can change in hours or days of sitting around. I mention this as a possible way to use fresh tap water in the new tank. By that I mean fill the new tank and let it sit with filters running to make sure all is well. I do this to give time to get the heaters adjusted if needed. Also is easier to take care of any problems without fish in the tank. May turn out the water will be a closer match to the old tank.
The general understanding I glean form experience and reading is fish deal with pH as long as it is not a sudden change. Another possible way to deal with possible differences in the new setup is the same way many of us use when bringing in new fish from a shop. I acclimate all the new fish slowly. Methods may vary.
Usually I have new fish in a bag of water. I float the bag for a while so temps can equalize. I then start adding some tank water into the bag a little at a time. After adding the tank water enough to suit I then pour out the bag water into a bucket thru a fish net. I catch the fish in the net and then put them in the tank. That last step is so there is a reduced chance of adding something unwanted to my tank. You are moving your own fish so could skip this las step I guess.
Let me add an observation which may or may not be valid. We have test kits for several water parameters. I sometimes get an impression many only pay attention to those things we can measure. I figure there will be a lot of other things in the water of a mature tank. Things we can not yet quantify. In past decades I did not take much caution when moving fish around from and into my home tanks. Best I can recall noting it worked well. I do recall fish taking a while to start acting normal sometimes, but they did settle in. I guess I am saying I never had fish go belly up from such a move. I guess it will depend on what the fish means to me as to how much extra care I might use.
That said there have been emergencies where I had to scramble to get fish into water and the fish did well enough. Say a cracked tank with nearly all the water leaked out.
Use as much care as makes you comfortable and good luck.