quinled.info is a website about DIY WiFi and Home Assistant controllable LED dimmers and controllers combined with lots of general information about LEDs and LED strips.
At least some WEMOS D1 minis have a 500mA fuse, limiting the power output. The mini can in theory use 250mA with everything used at full usage, but in most cases with the usually used parts it is more likely to use 150mA at high usage. This should allow you to run 10ish WS2812B-eco LEDs directly off the board from USB power.
Bias lighting for a 27" monitor would probably require a LED strip length of about the size of a 25" monitor, which is 55.4cm x 31.2cm. So, 117.8cm for the top and sides or 173.2cm for all four sides. Using a 60LED/m strip means about 104 LEDs for all four sides, and about 15W (5V/3A) power usage using WS2812B-eco at full white.