ffmpeg conversion from h264 for webserver – Debian

I’m working on a system to record videos through RPi (picamera, h264 format), export (rsync) 10s segments of videos to a distant webserver, and trying to concatenate those segment into a single video file to read on the webserver.

Simplified code to record on RPi:

import os
import datetime as dt
import picamera

camera = picamera.PiCamera()
camera.resolution = (1920, 1080)
camera.framerate = 25
duration = 10 #sec

[...]

camera.start_recording(filename, format='h264')
while True:
    filename = get_timestamped_filename()
    camera.split_recording(filename)
    camera.wait_recording(duration)

camera.stop_recording()

For the conversion, I tried many options/searches without success. I can get the video (.ts, .mp4, .ogv, .webm) working on majority of web browser but never on ios/android (chrome/safari).
As example of test & fail with ffmpeg: https://gist.github.com/jaydenseric/220c785d6289bcfd7366

When I don’t try to concatenate but only convert those video:

ffmpeg -i input.h264 -profile:v baseline -level 3.0 output.mp4

I have the following output:

ffmpeg version 4.1.6-1~deb10u1 Copyright (c) 2000-2020 the FFmpeg developers
  built with gcc 8 (Debian 8.3.0-6)
  configuration: --prefix=/usr --extra-version='1~deb10u1' --toolchain=hardened --libdir=/usr/lib/x86_64-linux-gnu --incdir=/usr/include/x86_64-linux-gnu --arch=amd64 --enable-gpl --disable-stripping --enable-avresample --disable-filter=resample --enable-avisynth --enable-gnutls --enable-ladspa --enable-libaom --enable-libass --enable-libbluray --enable-libbs2b --enable-libcaca --enable-libcdio --enable-libcodec2 --enable-libflite --enable-libfontconfig --enable-libfreetype --enable-libfribidi --enable-libgme --enable-libgsm --enable-libjack --enable-libmp3lame --enable-libmysofa --enable-libopenjpeg --enable-libopenmpt --enable-libopus --enable-libpulse --enable-librsvg --enable-librubberband --enable-libshine --enable-libsnappy --enable-libsoxr --enable-libspeex --enable-libssh --enable-libtheora --enable-libtwolame --enable-libvidstab --enable-libvorbis --enable-libvpx --enable-libwavpack --enable-libwebp --enable-libx265 --enable-libxml2 --enable-libxvid --enable-libzmq --enable-libzvbi --enable-lv2 --enable-omx --enable-openal --enable-opengl --enable-sdl2 --enable-libdc1394 --enable-libdrm --enable-libiec61883 --enable-chromaprint --enable-frei0r --enable-libx264 --enable-shared
  libavutil      56. 22.100 / 56. 22.100
  libavcodec     58. 35.100 / 58. 35.100
  libavformat    58. 20.100 / 58. 20.100
  libavdevice    58.  5.100 / 58.  5.100
  libavfilter     7. 40.101 /  7. 40.101
  libavresample   4.  0.  0 /  4.  0.  0
  libswscale      5.  3.100 /  5.  3.100
  libswresample   3.  3.100 /  3.  3.100
  libpostproc    55.  3.100 / 55.  3.100
Input #0, h264, from 'input.h264':
  Duration: N/A, bitrate: N/A
    Stream #0:0: Video: h264 (High), yuv420p(progressive), 720x480, 25 fps, 25 tbr, 1200k tbn, 50 tbc
File 'output.mp4' already exists. Overwrite ? [y/N] y
Stream mapping:
  Stream #0:0 -> #0:0 (h264 (native) -> h264 (libx264))
Press [q] to stop, [?] for help
[libx264 @ 0x556885757980] using cpu capabilities: MMX2 SSE2Fast SSSE3 SSE4.2 AVX FMA3 BMI2 AVX2
[libx264 @ 0x556885757980] profile Constrained Baseline, level 3.0
[libx264 @ 0x556885757980] 264 - core 155 r2917 0a84d98 - H.264/MPEG-4 AVC codec - Copyleft 2003-2018 - http://www.videolan.org/x264.html - options: cabac=0 ref=3 deblock=1:0:0 analyse=0x1:0x111 me=hex subme=7 psy=1 psy_rd=1.00:0.00 mixed_ref=1 me_range=16 chroma_me=1 trellis=1 8x8dct=0 cqm=0 deadzone=21,11 fast_pskip=1 chroma_qp_offset=-2 threads=9 lookahead_threads=1 sliced_threads=0 nr=0 decimate=1 interlaced=0 bluray_compat=0 constrained_intra=0 bframes=0 weightp=0 keyint=250 keyint_min=25 scenecut=40 intra_refresh=0 rc_lookahead=40 rc=crf mbtree=1 crf=23.0 qcomp=0.60 qpmin=0 qpmax=69 qpstep=4 ip_ratio=1.40 aq=1:1.00
Output #0, mp4, to 'output.mp4':
  Metadata:
    encoder         : Lavf58.20.100
    Stream #0:0: Video: h264 (libx264) (avc1 / 0x31637661), yuv420p, 720x480, q=-1--1, 25 fps, 12800 tbn, 25 tbc
    Metadata:
      encoder         : Lavc58.35.100 libx264
    Side data:
      cpb: bitrate max/min/avg: 0/0/0 buffer size: 0 vbv_delay: -1
frame=  195 fps=0.0 q=-1.0 Lsize=     229kB time=00:00:07.76 bitrate= 241.3kbits/s speed=20.4x    
video:227kB audio:0kB subtitle:0kB other streams:0kB global headers:0kB muxing overhead: 0.687068%
[libx264 @ 0x556885757980] frame I:1     Avg QP:23.86  size: 24802
[libx264 @ 0x556885757980] frame P:194   Avg QP:22.46  size:  1067
[libx264 @ 0x556885757980] mb I  I16..4: 26.4%  0.0% 73.6%
[libx264 @ 0x556885757980] mb P  I16..4:  1.1%  0.0%  0.4%  P16..4: 20.3%  1.5%  0.6%  0.0%  0.0%    skip:76.1%
[libx264 @ 0x556885757980] coded y,uvDC,uvAC intra: 34.9% 54.4% 12.3% inter: 1.8% 12.4% 0.0%
[libx264 @ 0x556885757980] i16 v,h,dc,p: 45% 14% 17% 23%
[libx264 @ 0x556885757980] i4 v,h,dc,ddl,ddr,vr,hd,vl,hu: 35% 31% 11%  4%  4%  4%  4%  4%  4%
[libx264 @ 0x556885757980] i8c dc,h,v,p: 51% 17% 28%  4%
[libx264 @ 0x556885757980] ref P L0: 80.0% 10.6%  9.4%
[libx264 @ 0x556885757980] kb/s:237.75

But still, impossible to play on mobile web (iOS, Android)

Is there anything I’m doing wrong, either in the capturing process or conversion?
Do you have any recommendations?