Which things should be automated in a typical SaaS product for better efficiency or in general?

First answer a few questions:
a) which tasks takes most time and energy?
b) which tasks do you repeat many times?
c) how often do they change?
d) do they require personal touch?
e) which of them may be automated?

a) You should focus on saving time and energy. Worth to keep in mind is that, sometimes you don't need to automate something but just stop doing this.

b) If something takes you a little energy but occurs multiple times per day, probably should be automated. Bear in mind, you are losing most of energy on switching context. Small tasks are ones you can ignore very easily but the compounding effect in this case is a bi*ch.

c) Automation takes time in the front place. If something changes very often there's no point to automate this but rather think how to make it stable.

d) If something needs a personal touch, still may be automated but not to actually do the process, but support it. For example sales process is often based on relationships. You can use automation for gathering informations yours sales team can use later.

e) This is a tricky one because there's a chance you may be even not aware that something is possible. Because of that you should continuously extend your knowledge about tools and techniques. The fun part is: it's often not about a tool but an idea.

If you have all of this, you can start to play.

IMHO you can run your online business almost on autopilot, which means 95% of processes may not require any human.

The last things to keep in mind: Keep it simple.

Now a few examples:

Marketing:
Gather all content in Airtable - posts, newsletters, blogposts, podcasts etc. You can then use Integromat to share this content across different channels without need to login to your social media channels, blog or e-mail marketing platforms.

Design:
Use design systems and templates to keep your design consistent and scalable. With features like Components or Auto Layout in Figma, you can generate hundreds of creations with one click. There're also tools like BannerBear or Placid which may generate graphics based on data you provide.

Development:
Use no-code / low-code tools like Webflow, Airtable or Integromat. They're handy at early stage of product development and later to quickly test and prototype ideas before you add them to codebase of your product.

Beside that you can also automate sales, HR and PM processes.

Do you have any questions?

The whole point of software is to automated everything you can automate. If you must use humans in the loop this needs to be priced accordingly, but since humans are expensive and tough to manage -> automate where possible.