The wooden bath barrel stayed empty for a long time and is now completely dried up. The bands fall down. Is my hot tub now useless?

No, the barrel is not useless. You should:
* Place 3-4 screws into the wood, under the bands;
* Use short screws for it, so they do not pass through the side panels;
* If the bands are extremely loose, tighten the bands carefully until the side panels are evenly and firmly against the bottom;
* Fill up the barrel with 5-10 cm of water, the bottom must absorb the water slowly;
* Remember always to loosen the bands a bit;
* You need to loosen the bands depending on how quickly the wood absorbs the water;
* The wood does not absorb the water if the metal bands are too tight;
All these problems could be avoided if using recycled polypropylene inner inside the hot tub.