MacBook Pro 2020 with 2 x Dell U2518D monitors
Solution 1:
Your issue is very much like the one in this question about a MacBook with only two USB-C ports as well: MacBook 4K/60Hz adapter is working directly, but not via USB-C hub
While you have two Thunderbolt ports, the MacBook only had USB ports that supported DisplayPort. So, in your case, you have a couple of options:
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Plug one display into one of the USB-C ports and use the USB-C Hub w/ Power Delivery as described in the answer in the above linked question to connect your devices and your charger.
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Use a proper Thunderbolt 3 Dock. The problem that you're having with the Belkin Thunderbolt 2 dock is that while Thunderbolt is technically backward compatible, Thunderbolt 3 uses passive cables where as Thunderbolt 2 cables were active. A number of "high bandwidth" devices like storage and display require an active cable which the standard USB-C cables are not.
I recently wrote an answer about this for the question LG UltraFine & replacement Belkin USB-C cable gives blurry text. Basically all (quality) USB-C cables are Thunderbolt 3 cables. However, not all are active. Active Thunderbolt 3 cables carry power and cost about $50USD more than regular ones. I believe this is why your Belkin dock isn't working properly.
I would go with the first option: using the USB-C hub with PD. This gives you a lot of options out of the gate without spending too much money. If/when your needs outgrow the hub, go for the Thunderbolt 3 dock as you'll have much more room for growth.
You can try getting the active TB3 cable, but to me, it's more of a bodge and I'm not convinced the Apple TB3 to TB2 adapter carries power. There are lots of folks looking for Thunderbolt 2 docks because they have 2017 and older MacBook Pro laptops they'd like to expand but can't because of product availability; it could fetch a nice price online and help pay for that Thunderbolt 3 dock.
Solution 2:
The problem is with the USB-C -> USB-A connection you are losing your DP/HDMI video in the transition between adapters.
Ideally, you need a dock that provides a USB-C connector and runs USB 3.1 and/or Thunderbolt3 over it. USB-C is the connector it could be USB 3.1 or it could be Thunderbolt3. The Mac can send video over just USB 3.1 via USB-C without Thunderbolt. Buying a newer USB-C dock which can be expensive. You need to ensure the USB-C dock can provide enough power (wattage) to charge your MacBook Pro battery. Look at the side of your charger for the wattage your Mac uses. 63W/90W, etc. Thunderbolt3 is not required unless you need to plug fast Thunderbolt3 drives into the dock.
However, if you don't mind attaching two USB-C cables one for each monitor and a third for MacBook Pro power, then they are cheap and easily obtained online. Since both monitors are the same they should both have DisplayPort and HDMI ports. I would prefer DisplayPort over HDMI every time when driving computer monitors.
Search your online retailers for the following:
- USB-C to DisplayPort Cable
- USB-C to HDMI Cable