Does the community here have any recommendations for podcasts, blogspots, shiurim apps/websites etc. that cover Hilchos Shabbat? Particularly I’m looking for something that is English, understandable for non-Yeshiva people, and preferably covers it from both Halacha and responsa but also can tie relevant halachic questions back to the Talmud.
If by "etc." you include books, I can recommend some excellent ones. Since the laws of Shabbat are very extensive, it is unlikely you can cover all these laws in a structured way outside of books. And only books can be studied on Shabbat.
The classic exposition in English of the laws of Shabbat in a structured way is Shemirath Shabbath k'Hilcheta from R Yehoshua Neuwirth, it was first published in 1984 and updated/republished many times since. It covers all laws of Shabbat in a somewhat terse format, and serves as an excellent reference work.
More pedagogical and recent is R Daniel Braude's Learn Shabbos In Just 3 Minutes A Day. It is meant to learn and review the laws of Shabbat frequently and is broken down in daily one- or two-page chunks to make it easier to absorb. It also covers all laws, includes frequent modern illustrations, plenty of references and is very pedagogical. Highly recommended.
The more extensive but still user-friendy option is R Simcha Bunim Cohen's exposition of the laws of Shabbat. It covers all laws in English with extensive Hebrew footnotes for further study. It is a 7-volume set and represents a good mix of depth and user-friendliness. This is the closest to your requirement of "tying halacha with Talmud" as it frequently describes Talmudic disputes and how they translate into halachic opinions. It has an extension in the same format for the laws of Yom Tov.
Since many of the halachic references you will find in the above works will be to Shulchan Aruch and Mishna Brura, if you wish to go in more depth you will need an edition of SA/MB. An excellent one, with additional digests of the laws of Shabbat as they apply to modern times, is the Ohr Olam edition. It is an 8-volume set and exists in large and medium format. There is a 2-volume extension for the laws of Yom Tov.