Vostro 3671, what is the motherboard?

You don't need to know the motherboard model to add a video card. You can order a video card already installed when you buy the computer from Dell. That's better than adding a card after the sale but the models with discrete cards are more expensive but have upgraded hardware. Here is one--

https://www.dell.com/en-us/work/shop/cty/pdp/spd/vostro-5090-desktop/cav5090w10ph0117?gacd=9646510-1025-5761040-0-0&dgc=st&&gclid=Cj0KCQiAkKnyBRDwARIsALtxe7g2QV4Q5J1liMQ1hGi1clJUESez94V9jmciz_WEP7hYGqlHlKlZU6QaAoEiEALw_wcB&gclsrc=aw.ds

Check the manual here:

https://topics-cdn.dell.com/pdf/vostro-3671-desktop_owners-manual2_en-us.pdf

The Vostro is a business model. If you are a home user, consider an Inspiron instead.

https://topics-cdn.dell.com/pdf/vostro-3671-desktop_owners-manual_en-us.pdf

https://www.dell.com/support/manuals/us/en/04/vostro-3671-desktop/vostro3671_mt_servicemanual/working-on-your-computer?guid=guid-9ccd6d90-c1d1-427f-9e77-d4f83f3ad2b6&lang=en-us

There are VERY FEW cards that fit and work in the tiny case.

75W cards are not supported.  40W cards like the GT1030 work fine with secure boot off.

https://www.dell.com/en-us/work/shop/msi-gt-1030-2g-lp-oc-graphic-card-2-gb-gddr5-pcie-30-x16-low-profile-hdmi-displayport/apd/aa362018/graphic-video-cards

https://www.youtube.com/watch?v=2y32mBdZHJY

The board layout is non standard. And the 24 pin power connector is 8 pins requiring an adapter.

So you will not find any standard case.

https://www.dell.com/support/manuals/us/en/04/vostro-3671-desktop/vostro3671_mt_servicemanual/system-board-layout?guid=guid-07a9116f-7856-421d-a4dc-259de688de2c&lang=en-us

Micro ATX is close but its not exactly that.  The holes are not in standard positions.

Board is larger than MATX at the front

Micro ATX layout