If you want to see it, tickets are incredibly competitive. They are released in batches ahead of time on the official website (https://www.lastsupper.shop/en/). At the time of writing for example, the tickets for 1 May- 31 August was released on March 24. They typically sell out very quickly - personally I would be hitting F5 refresh on the website within a minute of release - like you would for Taylor Swift concert tickets. Website will have the exact time. Needless to say if you show up on the day, you have no chance of getting in. If you can't get tickets, see if you can do a tour to get in. But you will be paying multiple times the price.
From my personal experience, Last Supper tickets are the hardest to get save the Ceremony of the Keys in the Tower of London, Vatican Scavi and CERN tour.
What about the visit itself? Honestly it's very brief. You are herded through climate control air lock with others in your group. And you are only allow a few minutes there. There is an app for the visit that you can download ahead of time. The painting itself is in very poor shape. But personally I am glad I got to experience it in person - cause I like art.
Verdict: if you are a huge admirer of Italian Renaissance or Leonardo and has a bucket list to tick off every one of his painting (except the Salvator Mundi held on a Saudi prince's yacht), then it is a must. However, if you have only have a passing interest then possibly not, as the experience is rather limited.
I find the Basilica di Santa Maria delle Grazie next door much more rewarding (and less competitve). The Castello Sforzesco is also nearby. Combined all three on the same day to avoid wasting time criss-crossing the city.

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