Creative suite 6

You can't.  Legacy Creative Suite will NOT run on Catalina or Big Sur.  You need modern 64-bit software now.  Or you need an old Mac with an old OS on it and freeze it in time by never upgrading it.

MODERN OPTIONS:
Photoshop Elements or Premier Elements (approx $100, no subscription needed)
https://www.adobe.com/products/photoshop-elements.html

Creative Cloud Photography Plan -- approx $10/month for 12 months. Includes the very latest versions of these great products & services:
-- Photoshop CC and Photoshop on iPad
-- Lightroom on desktop, mobile and the web
-- Lightroom Classic
-- Portfolio website + hosting
-- Spark with premium features
-- Bridge
-- 20 GB cloud storage (upgradable to 1 TB).
https://www.adobe.com/creativecloud/photography.html

Creative Cloud All Apps (31 + apps & services) and Single Apps Plans
https://www.adobe.com/creativecloud/plans.html

All Adobe software was 32 bit, or contained 32 bit components, right up to CC 2019, including all Creative Suites.

After a decade of reminders to developers and 3 years of warnings to end users in Mojave etc, Apple fulfilled their promise and finally modernised by dropping all support for all 32 bit components in Catalina and Big Sur. It's all 64 bit software only now.

So, there is no possibility of running any software containing 32 bit code in Catalina or Big Sur. That includes Creative Suite 6.

"installer needs updating" is Big Sur's way of saying it's found 32 bit code that it cannot understand or run. It needs 64 bit code. The CS6 installer will never be updated to 64 bit.

No, it's completely impossible. Catalina (the system before Big Sur) deliberately blocked all old apps. You need to get up to date. Creative Cloud, subscription only. 

I've moved this from the Using the Community forum (which is the forum for issues using the forums) to the Download and Install forum.

Probably not. Some CC apps are having issues.