I am sorry to hear that Max seems subdued, has a possible kink or lump near the base of his tail, and isn't happy with his tail being handled.
I am pleased to hear that he is eating and seems to be able to jump normally.
The most common causes of tail discomfort where a kitty can still move his tail but it hurts to do so are bite or scratch wounds to the base of the tail or tailhead area or anal gland infections or abscesses. These kitties have normal neurologic function, it just hurts to move the tail. I would try to examine his back near the base of his tail, the tail itself and have a peek at the area around his rectum to look for swollen or abscessed anal glands. Perhaps he sustained a bite to his tail, or took a fall when he was outside causing damage to his tail.
It is worth looking at the swollen area, pushing aside the fur to look at his skin for signs of a bite.
If a bite is present then clean the area thoroughly with a dilute solution of warm water and antibacterial handsoap and have him see his veterinarian in the morning.
If there isn't any sign of a bite you can take a watch and see approach. We do not attempt to splint or repair a broken tail. It is too difficult to do, and can cause more problems with loss of circulation if we try bandaging a tail.
Keeping him quiet and taking a watch and see approach may be best if you don't see any evidence of a bite.
Since he goes outdoors another possible cause of his discomfort is a tail pull injury or tailhead trauma.
This occurs when a cat falls and lands on his tailhead/back of the pelvis or the tail gets caught (by another animal or a car) and pulled hard enough that the caudal spinal cord is stretched. Sometimes the nerves are just stretched, but in some cases they break and when that happens the damage can be permanent. Cats may not show the full extent of their injury for several days as secondary inflammation and nerve death occur. Treatment is with steroids and rest.
If he is having trouble passing urine or stool he should be seen by a veterinarian as soon as possible. But if he is able to eliminate normally I recommend that he be closely confined and then see his veterinarian tomorrow if he remains uncomfortable.
They can examine him and prescribe antibiotics is a bite or scratch wound or anal gland abscess or infection is found, or they can prescribe anti-inflammatories if it appears this is a spinal cord injury.
If testing at your veterinarian is nondiagnostic you may want to discuss further testing with your veterinarian as well as referral to a veterinary neurologist for an MRI.
Increased drinking should not be related to a tail injury, but perhaps he got a bit dehydrated with all of his activity.
Best of luck with your fellow, please let me know if you have any further questions.