There's a download button in the top right, when viewing a page in a magazine. For example, you can go to Study.ChurchofJesusChrist.org > Magazines > Liahona > May 2021, then click the download button in the top right, then choose "Entire Book (PDF)".
The web and app text is usually available before the PDFs, so July 2021 isn't available yet. I'm not sure why June 2021 isn't available (I would have expected it to be available by now). If you're looking for June, you could try sending feedback using the feedback link at the bottom of the Church website.
Samuel Bradshaw • If you desire to serve God, you are called to the work.