No.  The resident labour market test has been abolished.  This means there is no requirement on employers to advertise the role to demonstrate there are no suitable settled workers, or that the person who will be sponsored is the most suitable candidate for the role.  This will reduce recruitment lead-in times by up to around one month in many cases.
However, Appendix D of the Skilled Worker sponsor guidance has recently been amended to state that evidence of any recruitment activity undertaken for a job must be retained, even where the RLMT does not apply.  The relevant evidence to be retained is essentially the same as it was under the previous Tier 2 (General) regime, including screenshots.  Appendix D also states that if the role was not advertised, the sponsor must be able to explain why it was not advertised and how the sponsor identified that the individual was suitable for the role.
The recent amendment to Appendix D is unexpected and puts sponsors in a difficult position in deciding what paperwork should be created and retained.  Pending further clarification, where roles are advertised and a selection process has been undertaken, sponsors should continue to retain paperwork from the advertising and selection process in a similar manner to the previous Tier 2 (General) rules.  Where a role was not advertised, sponsors should ensure they are able to explain the reasons for this and why the migrant was appointed (eg, by retaining a memo on file recording this).