Is there a standard for water bottles? It's prudent to use water bottle cages that will adapt to bottle diameters within some range, to allow using multiple bottles in the same cage.

Naturally, this flexibility is to be hedged against safety. If the bottle needs to be squeezed in or out, that just distracts from the road.

In any case, I ordered a water bottle cage that turned out to have a fixed diameter of about 2 3/4", or about 70mm. A smaller bottle will rattle, and the full circle enclosure won't allow anything bigger.

A fixed size might be a good thing. If there exists some international / conventional size for bike water bottles, then a perfect fit will ensure that pulling a bottle and returning it can be done effortlessly (and hence safely).

Does such a conventional diameter exist?

I'm rather partial to metal containers glazed with ceramic, since these guarantee they won't react with the water, but since these seem to be available only in carabiner format that's not suitable for cycling, I'll have to settle for plastic bottles.

Update (following Carel's answer)

After two searches it's clear which brand Carel means. A big advantage is that those bottles are indeed listed as having ⌀ of 71, and so perhaps there does exist some convention at that diameter.

There are also stainless steel bottles from other makers, which should be perfectly safe, as well as ecological since they would last forever (unless/until lost).

I see an ISO standard for bikes and another for bottles, but no ISO standard seems to exist for bike bottles.

Update (following Vladimir F's answer)

It's nice that the standard size is quoted in a wikipedia article (though without references). I wish the manufacturers were notified of the existence of this convention. Cycling aside, it would be nice if knapsack makers also followed the same convention.

As for getting a bottle-cage pair as one product, I'm not crazy about getting bottles and holders from the same maker, because I would have a hard time deciding what's better, to get a bottle from a bike maker or to get a cage from a bottle maker.
Product recommendations are generally not the thing here. There is however a reputed 4-letter Swiss company that has been producing internally glazed aluminium water bottles especially for cycling, properly fitting in standard bottle cages for many decades now.

And since it is Swiss it will certainly go on for much longer. The problem however with internally glazed metal bottles is their relative fragility. cycling bottles tend to be dropped and hard contact with the ground damages the coating which makes the bottles expensive garbage.

Most modern plastic bottles no longer have that specific 'plasticky taste' that cycling bottles used to have and can be used without restriction. Also all companies produce recyclable ones and some are even biodegradable after some months when lost in the outdoors, if this helps to lighten your conscience.

Concerning cages: cages that have a certain flexibility and that are slightly tighter keep a much better hold of bottles on rough terrain. When pros ride on cobbles the team mechanics often stick strips of skateboard tape to the cages to give the bottles a better hold.