Give a list a default status
Make a column set a job's status automatically when you drag something into it.
A list on a tracker board can carry a status. When it does, dropping a job into that list sets the job's status for you, so dragging a card left to right through your pipeline keeps everything correct without opening a single menu.
Setting it
Open the menu on a column header and choose the status that column represents. You can also set it from your tracker settings, where every list is shown together, which is easier when you are setting up a board for the first time.
The six lists you start with already have sensible statuses set.
Lists without a status
A list does not have to carry one, and leaving it blank is a real choice rather than an unfinished setting.
If you organise your board by company, or by priority, or by anything other than stage, then your columns are not stages and should not overwrite anything. Dropping a job into a list with no status leaves that job's status exactly as it was.
You can mix the two. A board of company columns plus one "Not Selected" column will set the status where you asked for it and leave it alone everywhere else.
What it does not do
Changing a list's status only affects jobs that arrive afterwards. Jobs already sitting in the list keep the status they had, so relabelling a column will not silently rewrite your history.
If you want those jobs updated too, you can select them and set the status yourself.
Why the status lives on the job
Because the column a job sits in and the stage it is really at are not always the same thing. Keeping the status on the job means renaming or reorganising a board never changes your dashboard numbers.