Hello I hail from the Uk but I do enjoy watching video recordings of usA court proceedings (I'm a fan of Sovereign citizen failure videos)
In these clips, it appears that there are people hired and appointed as 'the court bailiff'. They generally seem to be under the command of the presiding judge and can be asked to under take many different duties ( calling the court to order, etc.), or simple tasks such as bringing documents up to the judge if needed. In some of more 'excitable' videos I've seen it sometimes also includes taking people into custody for contempt of court or managing the security of court should a witness or defendant get out of control.
In the UK, a court-appointed bailiff is a very different role, and 'bailiffs' are often people the court appoints when there is a debt due, and the applicant wants to have the defendant's assets seized, or in housing court, if a landlord wants people evicted from a property so they are still the court's appointed 'physical muscle' as such, but they are mostly used outside of the court room. I'm looking to see if there is a UK version of the role I describe earlier, essentially an officer that is present within the court room to deal with such matters as unruly participants/ detaining people if needed.