macOS 10.15 (also called Catalina) was released October 7th 2019.

Logger Pro 3.15: runs partially, but all video functions, Vernier-branded spectrometers (all Spectrovis, Vernier Emissions Spec), Ohaus balances, Watts Up, and WDSS do not work.

Version 3.15 has been notarized to install and run in macOS 10.15; no other version of LP has been notarized. Detection of notarization by Catalina requires an internet connection. Version 3.15 can be used successfully for most purposes, with the caveats above regarding video and certain devices.

In short, if you are running macOS 10.15, you should use Logger Pro 3.15 only, and you will not have access to video functions, certain spectrometers listed above, and other less common devices.

Because of significant development work needed to run Logger Pro in macOS 10.15, there will be two releases of Logger Pro in early 2020: one to allow data collection (a beta build is available now on request), and another to support video analysis. These releases will follow the release of macOS 10.15 by possibly several months, so if the use of Logger Pro is important on a particular machine, do not update the OS.

Graphical Analysis 4.10: no major issues exposed at this time. Graphical Analysis has been notarized for Catalina.

Spectral Analysis 4.8.4 was released on September 24, 2019 to support USB connections to spectrometers on Catalina, as well as to include app notarization.

See also:
macOS gives a message on launch of Logger Pro that "Logger Pro has not been optimized for your Mac"
Video capture does not work in Logger Pro under macOS 10.14 Mojave or newer.
macOS is warning me that Logger Pro is not 64 bit and therefore won't run on 10.15 Catalina