engine "gost" set.
CONNECTED(00000003)

>>> ??? [length 0005]
16 03 01 00 b4

>>> TLS 1.2Handshake [length 00b4], ClientHello
01 00 00 b0 03 03 74 24 6c 60 b3 9c 1d 3e 6b 74
27 72 c0 f2 c5 c7 39 f6 c8 73 5c a1 04 de b8 b9
de 47 bb 46 df 78 00 00 38 c0 2c c0 30 00 9f cc
a9 cc a8 cc aa c0 2b c0 2f 00 9e c0 24 c0 28 00
6b c0 23 c0 27 00 67 c0 0a c0 14 00 39 c0 09 c0
13 00 33 00 9d 00 9c 00 3d 00 3c 00 35 00 2f 00
ff 01 00 00 4f 00 0b 00 04 03 00 01 02 00 0a 00
0a 00 08 00 1d 00 17 00 19 00 18 00 23 00 00 00
05 00 05 01 00 00 00 00 00 16 00 00 00 17 00 00
00 0d 00 20 00 1e 06 01 06 02 06 03 05 01 05 02
05 03 04 01 04 02 04 03 03 01 03 02 03 03 02 01
02 02 02 03

<<< ??? [length 0005]
16 03 01 03 ec

<<< TLS 1.2Handshake [length 0051], ServerHello
02 00 00 4d 03 01 5b 3e 65 ff 56 09 22 1f 5d 4d
5a 3c c2 85 29 9a 64 34 bb e0 3b 0f 0b 75 08 b0
f5 06 5a f3 63 a5 20 61 f8 40 ea 34 06 df fc ca
1f a3 a8 31 38 d2 aa fb 8e 20 66 58 a4 e9 23 2f
9f b9 7b 08 9a 00 18 00 31 00 00 05 ff 01 00 01
00

>>> ??? [length 0005]
15 03 01 00 02

>>> TLS 1.0Alert [length 0002], fatal illegal_parameter
02 2f

140385060737472:error:141710F8:SSL routines:tls_process_server_hello:unknown cipher returned:ssl/statem/statem_clnt.c:1028:

---
no peer certificate available
---
No client certificate CA names sent
---
SSL handshake has read 1009 bytes and written 192 bytes
Verification: OK
---
New, (NONE), Cipher is (NONE)
Secure Renegotiation IS NOT supported
Compression: NONE
Expansion: NONE
No ALPN negotiated
SSL-Session:
Protocol : TLSv1
Cipher : 0000
Session-ID: 61F840EA3406DFFCCA1FA3A83138D2AAFB8E206658A4E9232F9FB97B089A0018
Session-ID-ctx:
Master-Key:
PSK identity: None
PSK identity hint: None
SRP username: None
Start Time: 1530815999
Timeout : 7200 (sec)
Verify return code: 0 (ok)
Extended master secret: no
---

0x5555558558f0 "\002"

openssl s_client -connect tlsgost-2001.cryptopro.ru:443 -showcerts -msg -debug -status -tls1

openssl engine -vvvv
openssl engine -t -c

.....
.....
Hello. After the commit ad74ff0 it is impossible to load the GOST engine in OpenSSL 1.1.0h. The GOST engine is loaded via openssl.conf file. But now ssl_load_ciphers is invoked before openssl.conf file is processed and GOST engine is loaded. So ssl_load_ciphers doesn't register GOST cipher suites properly, and they become unavailable for TLS.
How must I initialize openssl now to make the GOST ciphersuites work? Thank you.

Yes, this is known to be broken in 1.1.0 too (as I noted in my original issue description above). There is no workaround at the moment, although you could try cherry-picking the patch in #5813 back to to 1.1.0 as a temporary measure.