I don’t see a need to distinguish between a prominent Buddhist king Ajātasattu (or Ajātaśatru as he is known from Sanskrit buddhist sources) - from an equally prominent Vedic king Ajātaśatru of the śatapatha-brāhmaṇa and the bṛhadāraṇyaka & kauṣītakī-upaniṣads, both having sons named Udāyī Bhadra(sena), and both having had mothers from Videha, both evidently having an interest in matters philosophical, both having lived within at-most a century or two from one another, and both having royal links to the Kāśi-Kosala-Videha kingdoms.
The only real hurdle here that I see is - how would it be possible equate the period of the brahmaṇas & early upaniṣads with the period of the historical buddha’s lifetime?
The brahmin-scholar Kātyāyana (who in the 3rd century BCE wrote the vārttikas, commenting on the grammar of Pāṇini) on Pāṇini’s sūtra 4.3.104 ‘purāṇaprokteṣu brāhmaṇakalpeṣu’ says “purāṇaprokteṣu brāhmaṇakalpeṣu yājñavalkyādibhyaḥ pratiṣedhastulyakālatvāt” that the yājñavalkya-brāhmaṇas were an exception to this grammatical rule because they are recent brāhmaṇas not much older than Pāṇini’s time. The yājñavalkya brahmaṇas are evidently a name for the śatapatha brāḥmaṇa (and/or the bṛhadāraṇyaka-upaniṣad which is a part of the śatapatha), and therefore they were also from the 4th century BCE which is when Pāṇini lived. If that was the case, it would stand to reason that it wasnt very old in the Buddha’s lifetime either.
But this goes along with my other postulate that the language of the historical Buddha (and his interlocutors) potentially had optional svara accents like the language described by Pāṇini - so we are probably not very far off the truth in considering the Buddha’s lifetime to be on par with the time of the early upanishads, the surviving texts of which are marked with the svara accents.
Also we have discussed elsewhere on this forum that Pauṣkarasādi was an Aupamanyava (a son or close descendent of Upamanyu). The śatapatha brāhmaṇa calls Mahāsāla Jābāla an Aupamanyava. The Chāndogya-Upaniṣad mentions a Prācīnaśāla Aupamanyava (commenting on which surname Śaṅkarācārya says ‘upamanyorapatyamaupamanyavaḥ’ i.e. “an Aupamanyava is an offspring/descendant of Upamanyu”) adding the epithets Mahāśālā (wealthy enough to live in a significantly large house) & Mahāśrotriya (i.e. a mantra-parāga or an expert in the vedas). The Jaiminīya-Gṛhyasūtra mentions an Aupamanyava as a teacher with great respect, for it prefixes the name with the honorific Bhagavān (… gauruṇḍiṃ gaurgulaviṃ bhagavantam aupamanyavaṃ kāraḍiṃ sāvarṇiṃ gārgyaṃ vārṣagaṇyaṃ daivantyam ityetāṃstrayodaśa…). These are all texts very likely composed within a century of each other - and to the same period belongs the historical Buddha. The language that they use is late-vedic sanskrit (nearly the same as pāṇinian classical sanskrit).