There is no current ALM version of any Chrome browser that supports the desktop client. In the past there was limited support in certain browsers (and it varied browser to browser and there was no standard as to which module, ie defect, requirement, test..that worked in a given browser and different modules worked in different browsers). The problem is that the full desktop client currently requires Active X components and those are only available in IE and not in the other browsers as Microsoft wont sell the license to other developers to use within their browsers, so we are limited to IE browsers currently or the ALM explorer (which is a browser agnostic client that allows the full usage of all functionality without the use and restrictions/limitations that an IT department may impose. Until such time as the ALM application goes full HTML5 compliant with no reliance on the Active X controls we will still need to use IE or the ALM explorer for the full functionality.
Microfocus recently updated their supported browsers section and now Edge version 77 and later is supported in IE mode. Microfocus has a KM document that is created for Enabling IE mode in Edge version 77 and later that allows it to be used as an alternative supported browser.
Also Microfocus is recommending the ALM Client Launcher now as the supported alternative to the ALM Explorer and this allows the files necessary to be downloaded and packaged for use with the Microsoft browsers in environments that have IT security issues acquiring the files needed. Just mentioning this as a work around as well if you are having permissions and otherwise IE issues.
Hope these help with your questions,