While I'm on board with your dislike of metagaming, I fundamentally disagree that 'taking a short rest straight after a long rest' is metagaming.
If I sit on my couch and watch TV for 6 hours, while recovering from being mugged, then after one hour of rest I'll ask the very reasonable question of, "Have I done anything strenuous this last hour?" If the answer is 'no' then I've just had a short rest and can spend hit dice. One hour after that, I ask again, "Have I done anything strenuous this last hour?" If not, then I've just had a short rest.
Although 2-3 short rests per adventuring day may by typical, it is neither a rule of the game nor a fundamental law of the game world. Your entire waking day may be rest after rest. If magic works such that you regenerate your casting power after one hour's rest, then that idle noble warlock could short rest, cast two spells in 12 seconds or so, short rest, cast 2 more spell, and so on, until he gets his well-deserved long rest after an arduous day of spellcasting.
Why? Because that's how Pact Magic works! That's how Ki points and Sorcery points and Superiority dice etc. all work. Pretending that they don't work that way just because you think it is somehow 'unfair' is your own bias.
Of course the events in the game world may conspire to make an hour's rest impossible, whether for any particular hour or for a whole day (the other side of the short rest mechanic), but ask yourself this: would those bears have attacked the party at breakfast if there were no short rest based PCs? Will the very existence of short rest PCs mean that the universe spontaneously creates PC-bothering bears at 59 minute intervals?
We've had a long rest, and get the benefits. At breakfast the ranger comes back with a brace of live rabbits that he trapped; he kills one, I kill the other, the halfling cooks them because stereotype. I also cast armour of agathys so, along with the hex I cast on my rabbit I have used both Pact Magic slots. The ranger, of course, had cast hunter's mark on the rabbit he killed.
One hour after I cast my last spell, I ask if we did anything strenuous in the last hour. If 'no', we have just rested for an hour; a 'short rest'! We get the benefits, which for me means I regain my Pact Magic slots. Why? Because that is exactly how Pact Magic works!
Is this 'metagaming'? No! It's how the world works! 'Resting' has benefits. If you have exerted yourself by using your spell slots, the way you get them back is by resting. This is not 'metagaming'! Random bears should not miraculously appear in order to punish some PCs for getting their breath back!!