What if the management asks to record daily Scrum and then audit it?

I think you already recognize it will impact the openness of the team. But let's start with the openness of management first.

• Have they been clear about the problems are they trying to solve through micromanaging?
• Have they acknowledged the problems it will create?
• Have they explained why don't they trust their employees to self-manage?
• Scrum Teams should frame and meet their own commitments every Sprint. If the higher-ups do not recognize this as evidence of success, have they explained why?

It's hard to say what the impact of requiring the Daily Scrum to be recorded will be.

However, the role of the Scrum Master in this situation is clear. The Scrum Master is accountable for "planning and advising Scrum implementations within the organization", "helping employees and stakeholders understand and enact an empirical approach to complex work", "removing barriers between stakeholders and Scrum Teams", and "causing the removal of impediments to the Scrum Team's progress".

If this was asked of me, the first thing I'd do is get a better understanding of why anyone wishes to audit the Daily Scrum. Audits are typically based around conforming to laws, regulations, or standards. Which of these laws, regulations, or standards and which specific requirements from those laws, regulations, or standards are being used to justify the need to record and audit a Daily Scrum? I suspect that there are alternative ways that will allow the organization to satisfy these requirements while not impacting the team's ability to have an effective Daily Scrum. The Scrum Master should be in a position to understand the requirements and coach the organization in ways to meet them that are consistent with agility (and Scrum, if that's the chosen framework).

If I were in your situation, I think I would flip my Linkedin flag back to "#opentowork".  This sets off a lot of red flags for me. 

But while I was still there, I would work with management to understand the need for the recordings and the audits.  I highly doubt that someone will review all of the recordings so their "team attendance" and "screen sharing" metrics will not be representative.  I'm also not sure what insights those metrics would provide.  What has to be shared on the screen?  Would sharing a meme count? Who is expected to attending because if they look for Product Owner, Scrum Master, or Manager to be in attendance, they do not understand the reasons for the Daily Scrum.  Also why would a historical record of the Developers planning their days work be useful? 

This entire premise screams "micro-managing" and complete misunderstanding of the Scrum framework.  As Scrum Master you have a lot of work ahead of you to change the perception and help "management" learn how to best interact with a Scrum Team.

The product owner should deal with management, and try educating them about Scrum and benefits organization can have if they will let Scrum go as intended. From your side you should treat it as impediment.