feat(browser-tests): use nwaku-style format for light push log

[adklempner]

Problem / Description

Vac-DST's Waku simulations are instrumented to detect certain events by parsing log lines from the nwaku container. Currently, we do not emit these logs on light push sent in our browser sim image

Solution

Add nwaku-style log for lightpush

Notes

• Depends on feat(browser-tests): simplify, refactor, update dockerized browser node #2623
• Related to #feat(browser-tests): add nwaku-style logs for browser simulations #2521

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Checklist

• Code changes are covered by unit tests.
• Code changes are covered by e2e tests, if applicable.
• Dogfooding has been performed, if feasible.
• A test version has been published, if required.
• All CI checks pass successfully.

[github-actions]

size-limit report 📦

Path	Size	Loading time (3g)	Running time (snapdragon)	Total time
Waku node	95.9 KB (0%)	2 s (0%)	714 ms (+42.61% 🔺)	2.7 s
Waku Simple Light Node	147.2 KB (0%)	3 s (0%)	834 ms (+34.46% 🔺)	3.8 s
ECIES encryption	22.52 KB (0%)	451 ms (0%)	168 ms (+3.17% 🔺)	618 ms
Symmetric encryption	21.96 KB (0%)	440 ms (0%)	173 ms (-0.38% 🔽)	612 ms
DNS discovery	52.12 KB (0%)	1.1 s (0%)	498 ms (+59.5% 🔺)	1.6 s
Peer Exchange discovery	52.82 KB (0%)	1.1 s (0%)	287 ms (-22.69% 🔽)	1.4 s
Peer Cache Discovery	46.57 KB (0%)	932 ms (0%)	398 ms (+24.43% 🔺)	1.4 s
Privacy preserving protocols	77.02 KB (0%)	1.6 s (0%)	372 ms (-43.61% 🔽)	2 s
Waku Filter	79.65 KB (0%)	1.6 s (0%)	499 ms (+6.63% 🔺)	2.1 s
Waku LightPush	77.82 KB (0%)	1.6 s (0%)	498 ms (-6.25% 🔽)	2.1 s
History retrieval protocols	83.58 KB (0%)	1.7 s (0%)	657 ms (+19.05% 🔺)	2.4 s
Deterministic Message Hashing	28.88 KB (0%)	578 ms (0%)	142 ms (-52.24% 🔽)	719 ms