when i first read this, it wasn't clear to me either, but after testing i found that it is no problem at all to produce repair packs ANYWHERE IN THE NETWORK and have them accessible in any logistic chest (or in a roboport or in a repair turret) which does NOT NEED TO BE NEARBY, only be part of the network. when they are needed, the repair turret will "instantly teleport" the required "charge" of them and the unused part will stay where it was. thus it is much faster than bots flying back and forth through the entire base to transport and/or use repair packs.
if you already have bots, one of them might simultaneously start trying to repair and grab a pack, but soon give up and return that one repair pack to a roboport as it is usually done, and thus you might think that bots transport packs.
idea for improvement: having a mod option to disable bots from repairing (and thus unneccessarily flying around and back) when you want to fully rely on repair turrets instead of bots for repair. then they could concentrate on what they are good at: replacing destroyed buildings :-)
another idea for improvement: roboports have connection range 25 and areas 50x50 and 110x110, so that it is easy to build the next roboport at or "right behind" the edge of the current one's area (including power poles etc), but repair turrets have the same connection range and only a construction range of 50x50. it would make some things (eg building lines of turrets, or later replacing 2x2 turrets by one roboport) easier if they would have more than twice the area of the connection range (>50 = 2x25), maybe at least half of the roboports' construction range (>=110/2, 55 or 56 instead of 50).
TLDR: you don't have to deliver the repair packs to any turret yourself or by bots which would cost time. it is done instantly and only might cost a bit of power (not tested that yet) depending on how far away the packs were and how many hops (intermediate turrets) they were relayed by.
@kreeg :
"Repair turrets will now consume repair packs to do the repair." - yes, you need to have them ANYWHERE (which should be no problem when the logistic network has access to copper and iron, minor problem when you want to protect an unconnected radar outpost or similar).
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"If they do not have any in their own repair slot, they will search the logistic network for one." - yes, and then (this could be phrased a bit clearer) instantly teleport the "charge" off of them and do the repair.
"...nearly identical to Roboports. They still require either manually inserting repair packs or bot delivery." - NO (a really BIG NO) : besides the different areas (logistic 0, construction quarter of roboport) and no storage space for bots, they do NOT need to slowly transport the packs or call bots for transport or similar slow methods. they directly teleport the required charges off them.