What specs are your PC? I've heard of Chrome being a resource hog but not so much Firefox. I'm no expert but I don't imagine that cookies would eat up a lot of CPU/RAM even if you hadn't deleted them in a while. Cookies are small files and shouldn't take up much space/memory.
How many plugins/extensions do you have installed? I would guess if you have a lot of them then that is your problem. Usually they are more demanding on your CPU/RAM. Gmail and Facebook are products of the largest advertising/tracking companies on the planet so yeah they won't give you an easy time. They desperately want to track your every move online.
What version of Firefox are you running? You can go to the hamburger menu > help > about firefox and it will say the version number.
If you want Firefox to remove all cookies then go to hamburger menu > settings > privacy & security > cookes & site data > manage data > and then click on the offending sites to highlight them (hold CTRL to select multiple) and remove selected (or "remove all" if you want to nuke everything).
As for tracking settings, strict is... strict. It will break some sites. In my experience it's mostly embedded content from sites. For example, on here if i have strict enabled it will block posts where people post shit from Twitter/Instagram. Running on "Standard" is fine. This shouldn't affect performance of the browser but more functionality.
I used to use CCleaner and then Bleachbit but instead what I do now is use an extension called "CookieAutoDelete" which you can find here:
Download Cookie AutoDelete for Firefox. Control your cookies! This WebExtension is inspired by Self Destructing Cookies. When a tab closes, any cookies not being used are automatically deleted. Keep the ones you trust (forever/until restart) while deleting the rest. Containers Supported
addons.mozilla.org
It is more advanced than using CCleaner/Bleachbit but what I do is run it alongside Firefox Multi-Containers:
Download Firefox Multi-Account Containers for Firefox. Firefox Multi-Account Containers lets you keep parts of your online life separated into color-coded tabs. Cookies are separated by container, allowing you to use the web with multiple accounts and integrate Mozilla VPN for an extra layer of...
addons.mozilla.org
What this does is let you group websites into containers. For example, I have containers for: Social Media, Forums, Shopping, Banking, and Google. So, for me, Reddit and Twitter are in the "Social Media" container. Reddit can see Twitter cookies and Twitter can see Reddit cookies. I have YouTube in Google container. YouTube won't be able to see the cookies of Reddit/Twitter as they are in different containers.
That said, you don't need to use Containers for CookieAutoDelete. CookieAutoDelete does what the name implies. When you vist a website you can whitelist cookies for that site so that it keeps them saved. I have cookies for Reddit, Twitter, Neogaf, YouTube, iCloud, Amazon, etc all whitelisted so I stay logged in at all times. For any site that isn't whitelisted the cookies will be deleted automatically after x amount of seconds. I think 15 is the default but I have mine set at 5. C.A.D will also delete shit like cache, localstorage, plugin data, etc.
I know I am rambling on and this is probably more advanced than you'd like (sorry lol). If you're having trouble with CCleaner then I'd recommend Bleachbit as a direct replacement and see if that helps any.
The thing is if you're using Gmail/Facebook then you're going to need to let them set cookies if you want to stay logged in. You could refuse to let them set cookies or auto delete them but then you'd need to manually log in all the time.
I'm done now I promise. I don't know if I've helped you lol but if you have any questions I'll try help you (and try keep it short!)