Sole traders are always self-employed but being a sole trader doesn’t necessarily mean you have to work alone. As a sole trader, yes, you can employ staff. There seems to be a bit of a myth, that you have to set up as a Limited business to employ people; this just isn't correct!
However, it’s important to bear in mind that you carry all the liability as a sole trader (given that you & your business don’t have a different legal identity).
You will need to register with HMRC as an employer & submit RTI (Real Time Information) submissions to HMRC. You may also need to set up an employer’s pension scheme, if they will earn £10,000 (for the 24/25 tax year) or more in your employment. This is known as ‘auto-enrolment’.
You should also look into statutory employment rights & make sure that you understand what your legal requirements as an employer are. In addition, you will need to get employers’ liability insurance. It’s also a really good idea to carry out background checks on anyone you’re considering hiring; you must check that they have a legal right to work in the UK for instance.
One thing I see self-employed cleaners doing all the time...
...is referring to sub-contractors (other self-employed cleaners that they work with, for their clients) as 'employees'. Please do not do this. They are sub-contractors, not 'employees'. People are only employees if they're on your payroll.