I can give you one example of it happening. My local history organization is the Oregon Historical Society. Early in the pandemic when things were shutting down they started a project for people to submit their personal experiences. People would be able to submit their experiences and it would be archived for future use.

Here's a link to the press release and if you click through to the form you can see what sort of information about demographics they collected to help future historians. https://www.ohs.org/about-us/news-and-press/upload/Stories-for-Historical-Record-Press-Release.pdf

That's one example for getting a good record of historical sources of day to day life. There are some issues with self selection in that. But it's an example.

At the other scale of it, you'll see a lot of this stuff from the National Archives people. They want people to write memos. They do oral interviews with people. They have trainings for people so they are creating proper records for future historians. That's a little different b/c if you're going to be President, or are working with the President, you have some idea of how anything you do might be historical. You can read their guidance in a little pamphlet they give to people coming into a new administration: https://www.archives.gov/files/guidance-on-presidential-records-from-the-national-archives-and-records-administration-2020.pdf

The most famous example of this that I can think of is probably the Library of Congress's oral history project. They have a few different ones. Most people are at least somewhat familiar with the Depression Era program to collect stories from the living people who had formerly been enslaved. But they also have projects on veterans and on American Folkways. They work with Story Corps to collect these stories and have a website on how to go about it, how to interview, and how to submit the stories, etc. Some of these projects are looking at more top down history by getting interviews with people who participated in some of history's big events (veteran project) and some are more bottom up history (folkways project.) https://loc.gov/folklife/familyfolklife/oralhistory.html

So historians do work with people to help create historical records.

You've gotten a couple good answers here, but I wanted to chime in with my own perspective. I'm an archivist and it's my job to collect primary sources for future historians and, less frequently, I also create primary sources for future researchers.

Other commenters have mentioned national archives. I'm not sure where you're located, but in the US, NARA is the arm of the federal government that keeps the nation's primary source documentation. But it's a huge effort! There are archivists hiding everywhere. You might have state archives, county archives, city archives, and a local historical society. Not all of them employ archivists, but they're all working to preserve and create primary source documentation of current events for future researchers.

A good example of this is the COVID-19 pandemic. In my job as a university archivist, I collected anything the university created having to do with the pandemic. But I also asked people to create things, like journals and photographs, among others, and deposit them in my archives. That became our COVID-19 collection and similar efforts were taken by many other cultural heritage institutions.

I am constantly looking to collect and preserve both old and new documents that illustrate history. Many archival repositories have collections scopes that guide what they collect, whether it's a specific era, subject matter, or something else. Those collections scopes help us decide what we collect, where we look for primary sources, what topics we include, and more. It's complex, but vital work. We miss stuff, but we do our best to collect and preserve primary sources for future people (history isn't just for historians!) so they can understand the past. I highly recommend checking the internet for your closest archival repository and paying them a visit. Archives are incredible resources and incredibly important.

Absolutely! During COVID-19 I organized an effort on our campus to encourage students to keep and later submit journals of their experiences, we set up web forms with a range of prompts to get students to share their experiences with COVID at the end of each semester, and in the fall we'll be doing oral history interviews with the seniors about their experiences from spring 2020 through this summer. I've also worked with our college archivist to ensure copies of all records, reports, media stories, and the material we are collecting are included in the college archives. I'm doing this in part because I've done work on the 1918 pandemic and found it very hard to find non-published sources in any real concentrations-- there are occasional diaries or letters but nothing systematic. So I've gone about doing pretty much exactly what OP asked about, i.e. imagining what might be useful to historians in 50-100 years and seeing what we can do to collect and archive it for future use.

Another example of creating primary sources is the Mass Observation project. Started in 1937 and revived in 1981 at the University of Sussex in the United Kingdom, the current iteration of the project collects information on daily life in the UK through surveys sent to a panel of volunteers. Writers receive 3 questionnaires a year, which include several open-ended prompts to respond to. The prompts tend to cover a wide range of topics; if, keeping within the spirit of the 20 year rule, we look at their Summer 2002 survey, participants were asked to write about how they celebrate their birthdays and talk about their experience with several current events, including the Queen's Jubilee and the war in Afghanistan.