Insert an array[4] to an array[8] (C++, SSE)
Storing

Are there other (better) ways to insert data from s2 into last four elements of peak_dB (AVX excluded)?

Yes, actually you already used that way: it's _mm_store_ps. For example:
    s2 = lin2db(s2);
    _mm_store_ps(peak_dB + 4, s2);

Maybe you prefer &amp;peak_dB[4] instead of peak_dB + 4, that works just fine too.
_mm_store_ps takes a pointer to wherever you want to store the data, that pointer does not have to point to the start of an array.
Loading
An other problem here is the use of _mm_set_ps. Though it accepts variable arguments, it is mostly meant for constant arguments, and good code is far from guaranteed if it is used differently. In the code on Godbolt, you can see the effect. Here I removed the code from lin2db from it that got &quot;interleaved&quot; into it:
    movss   xmm1, DWORD PTR float * channelsPeak+12
    movss   xmm0, DWORD PTR float * channelsPeak+8
    movss   xmm2, DWORD PTR float * channelsPeak+4
    movss   xmm4, DWORD PTR float * channelsPeak
    unpcklps xmm2, xmm1
    unpcklps xmm4, xmm0
    unpcklps xmm4, xmm2

And this is seen for the other similar instance of _mm_set_ps as well:
    movss   xmm1, DWORD PTR float * channelsPeak+28
    movss   xmm0, DWORD PTR float * channelsPeak+24
    movss   xmm2, DWORD PTR float * channelsPeak+20
    movss   xmm3, DWORD PTR float * channelsPeak+16
    unpcklps xmm3, xmm0
    unpcklps xmm2, xmm1
    unpcklps xmm3, xmm2

Avoid this pattern, try to use _mm_load(u)_ps if possible. That's easy in this case:
s1 = _mm_loadu_ps(channelsPeak);
// later
s2 = _mm_loadu_ps(channelsPeak + 4);

Zeroing
Initializing local variables of type __m128 like this is fine:
__m128 s1 = _mm_setzero_ps();

There's no serious problem with that, but it does not do anything useful in this code, it's just redundant. Of course if the value of zero is used as an input to something, then it should be done. But here it can just as well be skipped, declaring the variable only when you have a value to assign to it, for example:
__m128 s1 = _mm_loadu_ps(channelsPeak);