There is no detail about your environment and each environment can be very different so this general advice regarding the steps you should consider.
I think you should break down the migration into smaller tasks(update Joomla, update PostgreSQL, Upgrade to Joomla 4) and perform tests migrations on a copy of your site until you are sure it all works rather than try and do all of this in one go.
Update to Joomla 3.10.x
First clone your Joomla 3.3.6 site so that you have a working copy of your site that you can delete and start again if the update(s) fail. Whether you do that on a local machine or a different directory on your Hosting Account depends on your environment and skills.
Look at any extensions that need to be updated to work with Joomla 3.10.x and update them.
Because you are so far behind with Joomla 3.3.6 you may find you will have to find some older versions of Joomla 3.x and update through the various releases, Joomla 3.5 to 3.6 to 3.8 to 3.9 to 3.10 for example. Or you could just try and go straight to Joomla 3.10.x and if it works then you got lucky otherwise it might break your test site and you will have to either start with a fresh copy of your existing site to try and fix the errors along the way.
There are so many potential issues that could arise it is is near impossible to provide a simple 'do this, do that' set of instructions.
Once you have a working copy of your site on Joomla 3.10 you should back the test site up as a fallback position if the next steps fail.
You now have a choice to either replace your existing live site with the Joomla 3.10.x version of your site, which is how I would do it, or you back up your site 3.3.6 site again and go through the same steps to bring it up to date with 3.10.x now that you know what needs to be done. How often the data on your site is updated can have a bearing on which is the best way to go here.
Once you have a working Joomla 3.10.x site you can create a new clone and test updating the PostgreSQL version.
I am not familiar with PostgreSQL or your hosting environment to know whether you can run multiple version of PostgreSQL in the same account or what methods for migrating data from one version to another is required or if just restoring your Joomla 3.10.x back up into a PostGgreSQL 11.x environment is all that is required.
Upgrade Joomla 4
Now you can consider the tasks needed to migrate up to Joomla 4 but the steps are essentially the same, take a copy of your Joomla 3.10.x site elsewhere that you can work on and test upgrading to Joomla 4 and see what works and doesn't work and address those issues until you have a working Joomla 4.x that you can replace your live site with.