I am a manager in hospitality. When people are off sick it isn't the case a workload is divided out - it's a numbers situation where we need bodies on the floor.
As such, when people call in sick frequently and last minute I will admit I sometimes roll my eyes regardless of the reason. Only when it's frequent.
If someone submits a GP note for mental health and takes a period of leave I wish for nothing more than the person to feel better soon. It will cause us a day or two difficulty to cover the shifts but as it's only the first day that's imminent, it's usually quite doable.
I'm also very happy to work with people for long term sustainability - reduced hours, change of role within the business, phased return etc etc. I'm always more willing to do this when they hold up their end - ie. Say we will stick to 3 shifts a week whilst they find their feet, and they do actually turn up for them, give a different role and they genuinely try their best at it.
Taking a day - and calling in sick on the day - for a mental health day, honestly I hate this. I can see in a crisis why it's needed, but it's much better to speak before the crisis comes. Ask can we change some shifts for the next week to arrange some breathing space etc.
Communicate, commit to your end of any agreements, and plan to avoid burnout and I will help all the way.
Ring in randomly and frequently for mental health days here and there and don't work for solutions, my patience will wear thin.