Vienna advance tickets

Go to tge ticket website and try and buy tickets for tomorrow. See what you discover.

Yes, it is not required to buy tickets in advance. But entry to the museum is guaranteed only if you have an online ticket for a defined time-slot (of 15 minutes). If you are late you may be denied entry (unlikely).

If you just walk up there is a chance facing a line both at the ticket box and for entry, and you may not get a ticket for immediate entry, but for a time-slot somewhat later (or not at all for that day).

I have no recent knowledge whether this museum is overcrowded or not (haven't been there for a long time). Even if you do not a get a ticket for immediate entry, within five minutes of walking you are in the vibrant center of the city where you have the opportunity to spend your waiting time in numerous ways.

See all details here: https://www.sisimuseum-hofburg.at/en/

I was there only a couple of weeks ago and what we did was buy the combined Sisi Ticket in advance online that covers entry for the Hofburg Apartments/Sisi Museum (not the Imperial Treasury), Schoenbrunn Palace, and the Vienna Furniture Museum (in our case it was value for money even just to visit the first two, though near the end of our trip we did also visit the Furniture Museum and it was very interesting too). You can see details for the Sisi Ticket here: https://www.schoenbrunn.at/en/all-tickets/sisi-ticket

My understanding is that while you don't need this ticket in order to enter these sights, having it means that you're guaranteed entry at a time of your choosing without having to either wait ages in a queue to buy tickets, or wait ages for your specific timeslot, both of which can really eat up your time. If you're doing both the Hofburg Apartments/Sisi Museum and Schoenbrunn, I would say it definitely makes sense to use this ticket. It's valid for a year after you buy it and you can visit the sights any day you like, including on different days.

And regarding crowds, we did the Hofburg Apartments/Sisi Museum in the afternoon, and it wasn't too crowded; we also did Schoenbrunn a different afternoon and that was much busier (though it was also a Sunday so I don't know if it being a weekend affected the crowd sizes).