user8157: The new Sutta Central translations have translated the Pali word "sattā" as "sentient beings", as follows: 

And what is rebirth? Katamā ca, bhikkhave, jāti?
The rebirth, inception, conception, reincarnation, manifestation of the aggregates, and acquisition of the sense fields of the various
  sentient beings in the various orders of sentient beings.
Yā tesaṃ tesaṃ sattānaṃ tamhi tamhi sattanikāye jāti sañjāti okkanti abhinibbatti khandhānaṃ pātubhāvo āyatanānaṃ paṭilābho.
SN 12.2

What evidence is there in the Pali suttas that the word "sattā" means "sentient beings"? 

user10100: Yes, it is, if the sentient beings means dukkha-khandha (being) which still cycle-processing (sentient;paṭiccasamuppāda).
The being of asañña-satta is in the cycle processing, but asañña-satta has not nāma-paṭiccasamuppāda, so "sentient" shouldn't means sentiency. See Sutta. Aṅ. (4): sattaka-aṭṭhaka-navakanipātā sattāvāsasutta:

There are sentient beings that are non-percipient and do not experience anything, such as the gods who are non-percipient beings.
Santi, bhikkhave, sattā asaññino appaṭisaṃvedino, seyyathāpi devā asaññasattā. 


8157: <p>The new Sutta Central translations have translated the Pali word "sattā" as "sentient beings", as follows: </p>

<blockquote>
  <p><em>And what is rebirth? Katamā ca, bhikkhave, jāti?</em></p>
  
  <p><em>The rebirth, inception, conception, <strong>reincarnation</strong>, manifestation of the aggregates, and acquisition of the sense fields of the various
  <strong>sentient beings</strong> in the various orders of <strong>sentient beings</strong>.</em></p>
  
  <p><em>Yā tesaṃ tesaṃ <strong>sattā</strong>naṃ tamhi tamhi <strong>satta</strong>nikāye jāti sañjāti okkanti <strong>abhinibbatti</strong> khandhānaṃ pātubhāvo āyatanānaṃ paṭilābho.</em></p>
  
  <p><a href="https://suttacentral.net/sn12.2/en/sujato" rel="nofollow noreferrer"><em>SN 12.2</em></a></p>
</blockquote>

<p>What evidence is there in the Pali suttas that the word "sattā" means "sentient beings"? </p>
 10100: <p>Yes, it is, if the sentient beings means dukkha-khandha (being) which still cycle-processing (sentient;paṭiccasamuppāda).</p>

<p>The being of asañña-satta is in the cycle processing, but asañña-satta has not nāma-paṭiccasamuppāda, so "sentient" shouldn't means sentiency. See Sutta. Aṅ. (4): sattaka-aṭṭhaka-navakanipātā <a href="http://www.84000.org/tipitaka/read/v.php?B=23&amp;A=8534&amp;Z=8558&amp;eng=suttacentral" rel="nofollow noreferrer">sattāvāsasutta</a>:</p>

<blockquote>
  <p>There are sentient beings that are non-percipient and do not experience anything, such as the gods who are non-percipient beings.</p>
  
  <p>Santi, bhikkhave, sattā asaññino appaṭisaṃvedino, seyyathāpi devā asaññasattā. </p>
</blockquote>
