Handling a walk-in when the queue is full
A full bench is not a reason to refuse work. It is a reason to be honest about when.
Book it in
Take it in as normal. The job goes into Booked, which is the backlog, and it does not touch the bench until somebody picks it up. Nothing about a full workshop should stop a job being recorded.
Give a real date
Look at the week view before you say a day. The count on each column tells you where the pressure is; pick the first day that is not already heavy. A date you can keep is worth more than a date they wanted to hear.
Say what happens next
The customer gets a message confirming it is booked in, with a link to their own page. From that point they can check it themselves, which is what stops the call three days later.
If the item is unusable and they need it back sooner than you can do it, say so at the counter. Benchtop will happily record a promise you cannot keep; it just cannot keep it for you.