Here is the compatibility list for TP-link TL-MR3620 at https://www.store4g.com/blog/4g-modem-compatible-list-tplink-router/

Have you check the compatiblity of the Huawei E3372 modem with the TL-MR3420. If yes, please check the firmware version for it and update to it.

In general, there is no compatible issue for the smart plug with the Amazon Alexa. Have you ever try to use other common power adapter or try to restore your MR200 router to its factory setting?

I used a original SIM free Huawei E392u-12 modem and it work fine with the MR3220 router.

Now, the Huawei E3276s-500, E3276s-150, and E3276s-152 are supported by the TP-Link router.

It seems that the E398 Huawei modem isn't compatible with the MR-3420 fully. Now, just update the firmware to the latest, it could work without any problem.