The tl;dr is - I’m going to second and third (and fourth) the point that while you certainly can create a business entity to carry on any legal purpose, insuring it is likely to be a complicated mess if you group all these activities together in one business entity unit.
Now for more details -
There was a now defunct legal doctrine where you had to specify what the business was within the charter (or other founding docs), and you had to operate within that scope. That’s gone now in the United States, and all states will let you create a business entity that operates for “any and all” legal purposes.
The next piece is asking why you are creating a limited liability entity at all. There are basically 2 reasons why people choose limited liability entities - tax purposes & liability purposes. (Yes, there are other reasons. These are usually the two big driving purposes). Since more business entities have been created that allow you to choose your taxation now, it often becomes all about the limited liability.
Limited liability means that if you treat your business as its own entity, the assets/debts will be treated apart from your own on a personal matter.
Combining all these business purposes into one entity then means that any liability - creditors, debts, lawsuits, and so on - will trigger the entirety to be responsible.
The cost of insuring these types of businesses are extremely varied. Food safety has a specific set of rules/regulations and insurance liability expectations (because people can get sick or die). Working with animals has a different set of industry liability costs (because animals bite people and damage things). Being a fiduciary has its own liabilities (because people trust you with money you can lose). And so on.
Often insurance costs are determined based on the value or amount of revenue your business does. So let’s say you make $100,000 in tutoring and $100 in pet sitting. You absolutely don’t want to have to purchase professional pet industry liability insurance to cover the value of a $100,100 business. And if you group things together, you can be liable and on the hook for the entirety of that $100,100 for pet damage.
The recommended advice (Note - not giving legal advice here, every disclaimer!) would be to group like activities in their own entities and then be rigorous about your accounting so you never commingle the funds/accounts/records across businesses. It also would make sense to consider low risk/low revenue activities not even being worth the price of annual reporting/registrations associated with limited liability entities & just having decent personal umbrella liability insurance for that.