What is displayed at the bottom (or side, or spread between both the bottom and side for some cameras) of the viewfinder or Live View screen is usually determined by when the camera sets the exposure settings for a photo.
In automatic and semi-automatic exposure modes some cameras lock exposure as soon as metering is initially completed. In such a case the meter goes inactive after exposure has been set. Others wait until the instant the shutter button is fully pressed. Many cameras will do either one depending on what settings are selected at the time. Canon cameras, for instance, tend to lock exposure when metering is completed at the half-press of the shutter button when in the Evaluative metering mode but will continue to meter and modify the exposure settings right up until the time the shutter button is fully pressed in the other metering modes (Spot, Partial, Center-weighted Averaging, etc.) unless the Auto Exposure Lock (AE-L) button is pressed. Your Fuji X-T20 appears to do the same thing in Multi metering mode.
Most cameras display the current exposure settings, including exposure compensation via the +/- scale, when in an automatic or semi-automatic exposure mode. They will often display a +/- meter reading only when in Manual exposure mode. There are a few higher end cameras that have separate scales for exposure compensation, metering, and even flash metering or flash exposure compensation that can all be viewed simultaneously.
When exposure is locked in and the meter is inactive, the only way to update it is to reinitiate metering again. This can be done via another half-press of the shutter button, or by re-pressing an exposure lock button on cameras so equipped. When exposure is not locked then as long as metering is active the exposure settings and the display of them in the viewfinder will be updated.
In the case of your Olympus OM-D E-M10 Mark II, it seems that exposure is locked when the shutter button is half pressed (see page 53 of the E-M10 Mark II Instruction Manual) but apparently becomes active again when the half-press is released (per the statement in the question). Either that or you are shooting in Manual exposure mode with the Olympus.
Your Fuji X-T20 has a menu option called Shutter AE [Menu → Setup (wrench) → Button/Dial setting → Shutter AE] that allows you to select whether or not exposure is locked while the shutter button is half pressed (Please see page 227 of the X-T20 Owner's Manual). Setting it to Off should allow metering to remain active with the shutter button half-pressed. Page 154 of the Owner's Manual seems to indicate that using Multi metering mode will also lock the exposure settings as soon as the shutter button is half pressed. There are no indications at either location in the manual as to how the selected metering mode and Shutter AE settings may affect each other. If Shutter AE is set to 'Off' it may override the lock in Multi metering mode. Metering mode selections are only active when [AF/MF Setting → Face Eye Detection Setting] is set to Off. There's also no indication of how the various automatic exposure modes, such as the Scene modes, affect the settings mentioned above. Most cameras typically override all such settings in fully auto shooting modes.
Also note that the AF-L and AE-L buttons can be set to either lock AF or AE only while they are pressed or to lock AF or AE when they are pressed once and maintain that lock until they are pressed again (Please see pages 93 and 229 of the Manual).