Question regarding skilled worker start date and notice period

[newinswr]

Hi All,
I recently secured a job offer and switched to a Skilled worker visa from ICT.
I have one doubt.
My notice period with current employer will run into first week of Feb and it may not be possible to buy out as they may not have a replacement for me whereas my start date with my new employer defined in COS of skilled worker is mid of Jan.
Can I continue serving my NP with current employer after start date of my SW visa?
I did some initial research which suggests this may be the case.

On paragraph S3.9 and S3.10 of the linked document, it seems to suggest that I have until 28 days after my COS start date to join my new employer and I am allowed to serve out my notice period with my current employer
https://assets.publishing.service.gov.u ... -10-21.pdf


S3.9. You must normally stop sponsoring the worker and inform us via your SMS
account if the start date is delayed by more than 28 days after whichever is
the latest of:
• the start date recorded on the worker’s CoS (including any amendment to
that date you have told us about via SMS while the worker was awaiting a
decision on their application)
• the date the worker’s entry clearance (visa) becomes valid
• the date the worker is granted permission to enter or permission to stay
S3.10. An exception to this is where the worker is required to work out a contractual
notice period with their previous employer (and, where the worker is in the
UK, their conditions of stay allow them to do this). If, as a result of working
out a contractual notice period, the start date will be delayed by more than 28
days (as defined in the previous paragraph), you must notify us via your SMS
account. If you know the worker will need to work out a contractual notice
Page 21 of 55 Sponsor guidance Part 2: sponsor a worker - version 10/21
period, you should, as far as possible, factor this in when you enter the start
date on the CoS (but remember that the worker cannot apply for permission
more than 3 months before the start date on the CoS).


Could anyone please read through these and suggest?