If after enabling all the obvious things, it's still not working, try this:
In the Messages app, scroll to In-app Notification Settings & click
On that screen, scroll to In-app Notification Settings & click
Enable Preview new messages
THE ACTUAL FIX:
Use Edge Lighting in settings. I included another image below of what to expect (credit reverse image search).
Methods to Enable:
#1: Search for "Edge Lighting" under settings
#2: Click Settings > Display > Edge Screen > Edge Lighting > (choose apps or show edge lighting)
Requirements and More:
Required: Install EdgeScreen
Extra Customization: Install EdgeLighting +
Read: Samsung Use Edge Lighting
Note: All information provided using Galaxy S10 running Android 10.
Do you have edge lighting enabled on your device? With my personal Note10+ I only get the bubble pop-up when I enable the edge lighting option.
How frustrating that edge lighting can affect how you receive text notifications as if anyone would ever correlate the two and be able to solve this problem themselves. I upgraded from s7 and so far have been very disappointed with the s10. The screen scratches are insane (not a single scratch on my s7, first day of using s10 and deep scratches despite having a Samsung brand cover) you need to wrap the phone in bubble wrap to avoid scratches! The features are sub par, the keyboard is so bad but that could be the screen again as it doesn't respond well to touch, Bixby is useless all I get is "I'm sorry I don't know how to do that", I could go on but its it too hard to type and I'm sick of re typing what I'm trying to say cos predictive or auto correct wipes everything! I only use my s10 for calls & texts, I use my s7 for everything else!!