That's fantastic!
Yes it's a very traditional doublet, and unlike the modern "regulation" doublets which as you say look almost like a Prince Charlie with the tashes tacked on.
Of course doublets existed in a wide variety of cuts and lapel styles.
I did find one very similar to yours, with the leading edges of the tashes in line with the front opening of the jacket, and perhaps a similar number and arrangement of buttons:
Another doublet with the in-line front edges, but with deeper lapels and fewer buttons
Here with double-breasted waistcoat
Sometimes they're cut to hang open in a wide inverted V.
Hard to imagine it would be possible to button the lower buttons.
A piped one
Sometimes doublets are cut so that they can be buttoned
This doublet has the tashes set back slightly, giving a slight notch; it has your four buttons
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