Tip #1: Searching a website from the Google search box.
Tip #2: Finding recent articles
Simple Google searches are very effective. An example is: climate anxiety site:nytimes.
You might find it useful to make your search more complex to see if you get different results. You would do this by linking synonyms together with OR inside parentheses, and linking the parentheses together using AND.
Here's is an example:
(anxiety OR worry) AND (climate change OR environment OR global warming) site:nytimes.com
This would search for articles about climate anxiety and because it is a different method of searching, it might give you more or different results.
When you need more background and context on your topic, here are some good resources. They publish longer-form in-depth research reports on topics of current interest. These organizations are called research institutes or "think tanks". These are excellent sources of up-to-date research. Check their "About" page to make sure they say they are nonpartisan, like the ones below.
You can visit their sites or search them directly from Google. For example,
[topic] site:pewresearch.org
Some general search tips for finding research reports from NGOs, think tanks, and nonprofit research institutes
Tip: Always read the About page to understand who they are, why they are conducting the research, and whether they have potential biases
US government
California state government