Since you are a self-professed “newbie”, I’m going to assume that you aren’t really a skilled web programmer and up for integrating with the social platform APIs that would be required to produce your own bespoke all-singing, all-dancing solution. I’d also imagine that you wouldn’t be asking here. So that realistically leaves two options. Use a solution that someone else has produced, or streamline your existing manually intensive process.
The former is really more than automation and very much an architected solution. In the same way you would build a word processor application, rather than put together a few automations to try and give you the functionality … though if you start with a basic automatable word processor, admittedly you might bridge a gap on that. Before I get side-tracked too much on that particular tangent, you might want to have a scan through this Google Sheet of systems compiled by Buffer that compares several off-the-shelf options that could potentially serve your needs. There’s obviously an investment, but if a client is asking for more feedback, then it wouldn’t necessarily be unreasonable to factor in additional cost for delivering that as either you need to invest in a tool to reduce your time, or spend more time collating the information. That is over and above what you had previously been contracted to do.
In regards to the latter, it would be useful to know what sort of platforms you have access to use; but we can talk about things in broad terms to identify opportunities to have your process streamlined.
Zapier and IFTTT both have integrations for the social platforms you are referencing. There’s a potential there for you to set-up applets or zaps to trigger based on likes, replies, reshares, hash tag searches, etc. and feed that into any number of repositories - including Google sheets.
Since you are a social media producer, I would assume that you are using some tool for managing your postings. Such tools (e.g. Hootsuite, Agora Pulse, CoSchedule, Buffer, Sprinklr) often provide you with functionality such as scheduling, notifications and analytics. Depending upon what tool you use for this, you may have options where you can automate getting data out (or feeding in), such that you can then ultimately feed this in to your master Google Sheet - or some other location.
There are services available for each platform you mentioned that would allow you to convert sequential postings into RSS feeds. Once you have access to an RSS feed, there’s all sorts of web and local automation you can do to process the underlying XML. At the very least it could help you narrow down your postings for the day automatically … though depending upon your publishing tool maybe there’s an option to be feeding data into the tool so you are actually starting with your master list and are maybe only picking up further interactions with followers?
Depending upon what stats you want, on what social platform, and what your capabilities are with your local access platform are (iOS/Android/MacOS/Windows/Linux), you may be able to script your system to interact with your web browser and scrape data from the page to then feed into your master Google sheet. Tools like Shortcuts, Keyboard Maestro, Fake (browser), AutoHotKey, etc. can help facilitate at least some of this.
If the off-the-shelf platform isn’t a viable option, hopefully looking at automating distinct tasks and streamlining the overall process by tackling small steps in the whole process will be something you can adopt.
Hopefully that gives you a few ideas to consider about what direction you might like to go in, and perhaps some of the options you might consider around automation.