For Local SEO, you have to take care of the following things:
- Off-Page SEO / Link Building:
1. Local Business Citations With Real NAP (Name Address and Phone)
2. Press Release With Proper NAP (Name Address and Phone) and Brand Name in the title.
3. Google MAP Embeds in Press Release
4. Guest Posts and PBN Posts with targeted keywords in the content and GBP Embed in it.
5. Google Business Profile Optimization including Posts, Images, and unique content with keywords in it
6. Google reviews still playing a major role in ranking local businesses
5. Social sharing wouldn't work in Local SEO, per my experience but good to balance the overall campaign.
Let me know if you want On-Page and Technical details, and I'll share my experience.