Unable to update most of the new apps on my older workstation

#1  Legacy Creative Suite apps won't run on Catalina, Big Sur or Monterey. 

#2 CS6 is discontinued, unsupported and no longer available for purchase. And it has not been updated since 2012 when it came out so it's a decade out of date.  CS5.5 is even older.

To connect to Adobe's servers, you need an OS and browser that can support more secure TLS 1.2 connections.  TLS 1.0 and TLS 1.1 protocols are end of life now.  See link below.

https://helpx.adobe.com/x-productkb/multi/eol-tls-support.html

MODERN CODE EDITORS:
-- Adobe Dreamweaver CC - https://www.adobe.com/products/dreamweaver.html
-- Atom (free) - https://atom.io/
-- Codespaces (free, browser-based) - https://github.com/features/codespaces
-- Nova (Mac only, formerly called Coda) - https://nova.app/
-- Pinegrow - https://pinegrow.com/
-- Sublime Text - http://www.sublimetext.com/
-- Visual Studio Code (free) - https://code.visualstudio.com/
-- Wappler ~ Visual Web App Builder - https://wappler.io/

Hope that helps.

the main question is are you using specific DW 5.5 features, as Templates, Library item, Server Behaviors, Widgets, Spry Library...  in that case, you will be glue to older version of DW that was using those removed features... in case not , you can open DW projects with any new builds of DW but also with any code editor that you like VSC, ST, NP++, Coda, and so on...

if you have to stuck with DW 5.5, for the reasons detailed above, you can use a virtual machine as https://www.virtualbox.org/ it's free, and there you will be able to install and run an older Mac OS... as you already have a Mac, Mac on Mac is allowed by Apple... so you wont have a headache to install it... just clicking the go on and do it for me button...