Modern Site Page: Lists don't show up in List web part list

There are 3 separate issues here:

the original question was about lists being available on other sites which SP has never supported except with data view web parts.

"However, on other sites, it doesn't show the lists on the site:"

Joanne's response didn't address that problem but for some reason pointed to the second issue which mbsanchez has:

modern sites only show custom lists in the list picker

Problem 3 from JohnHamilton-Smith is about lists not showing up in the list picker which may or not be a different issue.

In a product as poorly implemented as SP Online with its many bugs and missing features,  it's especially important to clearly identify the issue.

"I'd like to explain that it is only supported to add custom list to List view web part on Modern site pages, other types of list such as task list will not show up there for we to add. "

In other words the modern sites are basically useless - trying to figure out what;s included and what isn't is a big waste of time. I'd ask what the rationale is behind this bizarre restriction is but i know I'll only get a mumbo jumbo answer so why bother. Stick to classic.

I am having the same issue re some lists not showing up

This is a modern Team site.

I created a list a month ago

Today I created another list

Only the list I created today is in the options for the List web part.

I have a Flow pointing to the first list adding in content from a Forms registration form, so I don't want to delete and remake the original list.

I changed a setting and saved to try and 'refresh'the list. No change.

I'm keen to expose a view of my registration list to show where people are signing up from.

I have the same problem. I can add web parts, and a custom list, but cannot see the vanilla announcement app or task list app that I created on my site.

I guess I can try to recreate my own version of a task & announcement list as a custom list and hope they show up.

Or should I create a new Classic site and make it my home page, then I can use the Classic Ribbon menu (below) to add app list and web parts?

Hi Mary,

I'd like to explain that it is only supported to add custom list to List view web part on Modern site pages, other types of list such as task list will not show up there for we to add. If this is your case, I'd invite you to submit your feedback in our SharePoint UserVoice to help improve our products. UserVoice is the best way for users to let related team understand your requirements and many features have been developed or upgraded based on users' comments.

We appreciated your understanding and thanks for letting us know we can serve you better.

If you did use custom lists and they don't show up when you try to add them to list view web part, feel free to post back and help provide the information below for investigation:

1.  Please go to Site Contents page on this site and help capture a screenshot of your lists.

2.  Please try creating a new custom list to see if you can add it to list view web part.

Regards,

Joanne