Free LastPass can only be used on one machine. It is the paid version that can be synched to other devices.
I have not tried it with password management programs (I have the sync version of StickyPass already that does sync) but the following works for me with FTP config files, files and photos, etc.
I have multiple computers and use a free program to copy files between systems, either copying the data one way or both ways. It is called Syncthing. I install SyncTrazor, configure it to either send, receive or send and receive files to the other system. For example, when I take a photo on my cellphone, it will be copied to my home PC as soon as there is a data connection or wifi link.My FTP program has a config files with encrypted passwords and if I add a computer connection to it, almost instantly the config file is copied to the other systems.
It cannot copy open files but once you exit the file, it can be copied.
This might be an option to do your own sync, especially if the password product wants to charge you to do the same thing.
You mean this article: Best Free Password Managers: 7 Top Picks (clark.com)
LastPass made a change in 2021 so the free tier syncs between only Android/iOS or only PC/mac. It works if you only have phones and tablets. In practice, most people want to sync between mobile and PC, so the free tier is not attractive now.
I think the article should also mention just using the browsers’ built-in password managers (Chrome/Edge/Firefox and iCloud Keychain), since all of them have beefed up their capabilities in the past few years.