As of Radeon Software Adrenalin 2019 Edition 19.1.2, ReLive overlay and recording functions are still not working in OpenGL and Vulkan games (e.g. osu!, Doom) running in Exclusive Fullscreen mode. Not sure if it's a bug or it has not been implemented yet. If it's the latter, please do implement it. ShadowPlay has had OpenGL and Vulkan support since May 2017.
Borderless Fullscreen is not an option for me as it adds massive input lag and makes fast-paced games unplayable.
CPU: AMD Ryzen 5 2600
MB: ASUS PRIME B350M-A
GPU: Radeon RX 580 4 GB
OS: Windows 10 Pro (1809; Build 17763)