Replace that HDD with a SSD, and that will help immensely. Better yet, have a SSD for OS, swap file, etc, and a separate SSD for recording to... but that is probably overkill (and often not possible/practical in lower-end consumer laptops).
That said, a 4th gen i7 is almost 10 years old, and way out-of-date for modern real-time video encoding. You could get a newer GPU for encoding offload, but probably not worth putting money into an older system like yours.
The issue is that some recording options (like chroma-keying a video camera input) or other plugins can have a huge CPU impact. So... it depends. You system, properly optimized, should be able to handle 720p ok, and maybe even 1080p depending on other workloads (ie, you can't max out the CPU and GPU with a game, then add real-time video encoding with OBS with lots of advanced features and expect that to work.) But a base workload that doesn't strain the PC, an optimized OS and OBS settings, and you might just get 1080p working.
To minimize load on your system,
- record and stream at same setting (so only 1 video encoding stream to process, vs 2)
- don't use Studio Mode as that 2X rendering workload
make sure you've optimized your Operating System but not running stuff that doesn't need to be. What that is? depends on you/your PC specifically
