Personally, I like the hackerrank or leetcode automated challenge as an initial first filter. It can be gamed by cheaters of course but that requires some work on the cheaters part. It allows me to start the test at a convenient time and in a standard format. Hopefully, it allows the company to be less stringent about skill sets and other resume keywords and simply test more people. Hopefully it makes job searches harder for resume spammers, cheats, and fakes. I suspect even a few really easy problems from these sites would be a useful filter.
Then perhaps a phone interview so that the company can confirm I'm likely not cheating.
Finally an onsite white board interview or written test or at the computer programming test. Yes I get nervous doing white board interviews but if the difficulty level of the problem is not too great it is a useful filter.
I dislike long take home work because it requires too much of a time sink and it could be abused by employers fishing for ideas, competitor information, or just wanting free work for one of their problem areas. Algorithm tests on hackerrank or leetcode or wherever are still useful practice but take home tests can be too job specific and therefore prematurely requires candidates to commit to learning a particular companies needs without the company committing anything in return.
Questioning candidates about their experience in an informal manner by conversation may be of some benefit, but is likely just testing how well the candidate has prepared various stories about their past employment and past projects. Unfortunately, abandoned projects that taught a candidate a lot and served their intended purpose may not make as good a portfolio or story as completed projects that were just cookie-cutter implementations of projects found in books or tutorials or elsewhere.
The important thing for all of these filters though is that they be carefully calibrated in difficulty to the companies needs and job sourcing pool. If your large top-N company carefully optimizes it's customer funnel with a/b testing but has no real employee hiring sanity checks, then that is not good. Randomly have one employee at the company white board interview another employee at the company from a different department. Secretly test your interview process with known good programmers from outside the company.