There is a possibility using a "Virtual Layer" through Layer > Add Layer > Add/Edit Virtual Layer...
Let's assume there is a polygon layer called 'test'
with its corresponding attribute tables, see image below.
With the following query, it is possible to get the bounding box for each feature in the source layer.
SELECT id,
ST_Envelope(geometry) AS geom,
ST_AsText(ST_Envelope(geometry)) AS geom_text,
-- XMIN,YMIN,XMAX,YMAX
x_min(ST_Envelope(geometry)) || ',' ||
y_min(ST_Envelope(geometry)) || ',' ||
x_max(ST_Envelope(geometry)) || ',' ||
y_max(ST_Envelope(geometry)) AS bbox
FROM "test"
The output polygon layer (grey) with its attribute table will look like