Did they change any brakes? Just a brake fluid flush?

That is pretty unusual for the parking brake to be effected from a brake flush. Unless they adjusted the rear parking brakes (depends on the car, some had plain rear drums, some are rear discs with an integrated drum) and/or adjusted the slack at the handle side of the parking brakes. I know that some shops will automatically inspect/adjust the brakes/tire rotation - as they tires generally have to come off anyways.

One click to drag is definitely too tight - I usually aim for 3-4 clicks, once it gets to 6-7 clicks then it gets a little too loose for my tastes.

Air in the brake line is a possibility - can tell by pedal feel. The brake pedal will feel "spongy" when depressed. If the brake pedal feel is firm - likely they took too much slack out of the parking brake cable and/or adjusted the rear parking brakes too tight.

Just brake fluid flush and no brake part replacement.

Will the click increase on the emergency parking brake handle when the brake’s pad & shoe wear down?

Yeah, as the brakes wear down - it will loosen up. But IMO, that is a pretty lousy way to approach that - as your brakes will be dragging slightly in the mean time.

These systems are self-adjusting - so every time you use the parking brake (ensures that the cable doesn't get too corroded) and backup from time to time (drum adjusting screw will turn slightly, pushing the brake shoes closer to the drum face) - there should be little needed in the way of routine adjustments.

Since they are tight - you will also be fighting that self-adjusting behavior. Only thing this will do is increase the amount of heat in the drums, could lead to issues like distorted brake hardware (clips, springs, etc. - most of the time, they are replaced with new brake shoes), warped drums, damage wheel cylinder (rubber seals), and of course - wiping what little friction material is already on the brake shoes.

I'd have them take another look - something is messed up. Or if you don't trust them - take them to a different shop. Since this is a critical safety related issue, I wouldn't just let this one slide by - for your safety and others on the road.