Is it necessary to perform ghusl and purify clothes and bedding, and make up missed prayers, in the event of doubt about the occurrence of something that necessitates ghusl during sleep or after waking up?

You are not required to perform ghusl unless you see semen that necessitates ghusl after waking up. Otherwise, ghusl is not obligatory for you.

If you see semen and have delayed ghusl, you must perform ghusl immediately and make up the prayers you performed during that period, because they are invalid due to the absence of the condition of purity.

As for the bed, bedding, and clothes, they do not need to be washed, because semen is pure, according to the prevalent opinion.