Nowadays if I was using a 4 track and a computer I'd probably just dump my 4 tracks into the daw and keep building in the daw. Although I have no idea if and/or how that would work, as I've never tried it.
You just need to sort out a sync box setup with your deck and DAW. You can get away with using the tape deck as master...just drop some SMPTE on one track before you start recording, make note of the SMPTE time where your song starts...then set that in the DAW time, and tell it to chase/lock to the SMPTE code coming off the tape. Of course, some DAW actually need the SMPTE converted to MTC...so they won't be able to use SMPTE just coming off the tape track as an audio signal...but then, a few DAWs out there can read pure SMPTE.
Anyway...that's the more crude way to sync, and it has limitations, because it's a one-way sync...the tape deck has no idea where the SMPTE is or how to read it...so it's all up to the DAW. Also, when a DAW is chase-locking, if the tape wobbles/lags...it could force the DAW to resample on-the-fly if there's a single break in the steady digitizing/recording of the audio tracks. That resample could cause glitches...and some DAWs do it better than other.
The absolute best way is for the DAW to be the master...for the sync to be two-ways, with both DAW and tape deck under SMPTE/synchronizer control.
Then you got a rock solid sync setup, and you can get very precise with doing all kinds of two-way record/playback actions.
Of course...it's a bunch more equipment and connections and configurations...and much of that is older, out of production stuff, so minimal to zero support...and sometimes it doesn't want to behave because of age old code in the microprocessors...so that's the price to pay.
I managed to get things to that level of sync, and it's a fully functional hybrid setup...but there are some days I think about the ease of just staying ITB...but so far I always end up hearing the reason why I still hang on the tape and the outboard stuff.
If I was doing like...EDM or more synth based R&B/Pop stuff, I would probably abandon the hybrid and go all ITB...but since I still track 90% of my instruments, and I don't do EDM or synth based R&B/Pop music...I'm not giving up the hybrid rig any time soon.
I also occasionally think about the old 4-track days when I used to spend a long weekend at home just playing and recording. My folks would head out of town, and I would have the house to myself...and it was a non-stop 3 day recording binge. I would write, record and mix a half-dozen songs some weekends, and every minute of it was fun. Most of it sounded like shit compared to now...but it was a lot of fun. Now days, recording and mixing is a lot more work if you want to really go for the best you can. There's so many tools...that you can't use the lack of as an excuse to just blow through your production like back in the old days when just getting the tracks down was the main challenge.