Thank you everyone for the replies.
I realize that my original post was perhaps too broad, but I wanted to get a feeling “IF it is possible” and HOW to go about it. I will continue trying step by step and slowly expanding my lab, until I get it right 
Speaking of which - I have a little progress. I narrowed my lab setup down to router CRS109 (GW) and one AP (CAP), which is a RB952Ui-5ac2nD (but I only pretend it has ether1 and wlan1)
On the router I setup VLANs, DHCPs and dedicated few ports as access ports and few as trunk ports.
What works - when I connect clients to access ports, they get an IP from the correct DHCP server and can browse the internet. From my perspective VLANs on router work as they should.
On ether6 I am runnign VLAN30.
- If I connect PC to ether6, everything works as expected (IP from VLAN30 range, connection to internet).
- When I connected the AP to ether6 and ran DHCP client on the AP (either on ether1 or the bridge), I do get correct IP assigned from DHCP (VLAN30 range).
- Then I removed the client and turned on CAP on wlan1 interface. It connects to CAPsMAN (running on the GW) and starts providing WiFi. I can connect to the wifi and get authenticated.
- (!) however, I do not receive an IP address.
(I tried different combinations assigning tagged/untagged to bridge, ether1, etc., but non of it was a success).
Here are my configs and I would appreciate if you can push me a little further so that I can get the wifi working. Thank you!
GW (CRS109):
# oct/24/2020 22:19:54 by RouterOS 6.47
# software id = WRL1-JR0T
#
# model = CRS109-8G-1S-2HnD
# serial number = 522D0463C99F
/interface bridge
add name=bridge
/interface wireless
set [ find default-name=wlan1 ] ssid=MikroTik
/interface ethernet
set [ find default-name=ether1 ] name=ether1-WAN
set [ find default-name=ether2 ] name=ether2-direct-notSwitched
set [ find default-name=ether3 ] name=ether3-Link1of2
set [ find default-name=ether4 ] name=ether4-Link2of2
set [ find default-name=ether5 ] name=ether5-vlan-open
set [ find default-name=ether6 ] name=ether6-vlan30
set [ find default-name=ether7 ] name=ether7-vlan-PC
set [ find default-name=ether8 ] name=ether8-vlan-raspberry
/interface vlan
add interface=bridge name=MGMT vlan-id=99
add interface=bridge name=VLAN10 vlan-id=10
add interface=bridge name=VLAN20 vlan-id=20
add interface=bridge name=VLAN30 vlan-id=30
/caps-man configuration
add country=slovakia datapath.bridge=bridge datapath.local-forwarding=yes \
datapath.vlan-id=30 datapath.vlan-mode=use-tag name=config_Work \
security.authentication-types=wpa-psk,wpa2-psk security.passphrase=\
123456 ssid=WiFiWork
/interface ethernet switch
set drop-if-invalid-or-src-port-not-member-of-vlan-on-ports="ether3-Link1of2,e\
ther4-Link2of2,ether7-vlan-PC,ether8-vlan-raspberry,ether6-vlan30"
/interface wireless security-profiles
set [ find default=yes ] supplicant-identity=MikroTik
/ip pool
add name=dhcp_pool0 ranges=10.10.10.2-10.10.10.254
add name=dhcp_pool1 ranges=10.20.20.2-10.20.20.254
add name=dhcp_pool2 ranges=172.16.16.2-172.16.16.254
add name=dhcp_pool3 ranges=10.30.30.2-10.30.30.254
/ip dhcp-server
add add-arp=yes address-pool=dhcp_pool0 disabled=no interface=VLAN10 name=\
dhcp1
add address-pool=dhcp_pool1 disabled=no interface=VLAN20 name=dhcp2
add address-pool=dhcp_pool2 disabled=no interface=bridge name=dhcp3
add address-pool=dhcp_pool3 disabled=no interface=VLAN30 name=dhcp4
/caps-man manager
set enabled=yes
/caps-man manager interface
set [ find default=yes ] forbid=yes
add disabled=no interface=bridge
add disabled=no interface=VLAN30
/caps-man provisioning
add action=create-dynamic-enabled master-configuration=config_Work
/interface bridge port
add bridge=bridge interface=ether5-vlan-open
add bridge=bridge interface=ether6-vlan30
add bridge=bridge interface=ether7-vlan-PC
add bridge=bridge interface=ether8-vlan-raspberry
add bridge=bridge interface=*10
add bridge=bridge interface=ether3-Link1of2
add bridge=bridge interface=ether4-Link2of2
/interface ethernet switch egress-vlan-tag
add tagged-ports="ether3-Link1of2,ether4-Link2of2,ether7-vlan-PC,ether8-vlan-r\
aspberry,switch1-cpu" vlan-id=99
add tagged-ports=ether3-Link1of2,ether4-Link2of2,switch1-cpu vlan-id=10
add tagged-ports=ether3-Link1of2,ether4-Link2of2,switch1-cpu vlan-id=20
add tagged-ports=ether3-Link1of2,ether4-Link2of2,switch1-cpu vlan-id=30
/interface ethernet switch ingress-vlan-translation
add customer-vid=0 new-customer-vid=10 ports=ether7-vlan-PC
add customer-vid=0 new-customer-vid=20 ports=ether8-vlan-raspberry
add customer-vid=0 new-customer-vid=30 ports=ether6-vlan30
/interface ethernet switch vlan
add ports="ether3-Link1of2,ether4-Link2of2,ether7-vlan-PC,ether8-vlan-raspberr\
y,switch1-cpu" vlan-id=99
add ports=ether3-Link1of2,ether4-Link2of2,ether7-vlan-PC,switch1-cpu vlan-id=\
10
add ports=ether3-Link1of2,ether4-Link2of2,ether8-vlan-raspberry,switch1-cpu \
vlan-id=20
add ports=ether3-Link1of2,ether4-Link2of2,ether6-vlan30,switch1-cpu vlan-id=\
30
/ip address
add address=192.168.99.1/24 interface=MGMT network=192.168.99.0
add address=10.10.10.1/24 interface=VLAN10 network=10.10.10.0
add address=10.20.20.1/24 interface=VLAN20 network=10.20.20.0
add address=172.16.16.1/24 interface=bridge network=172.16.16.0
add address=10.30.30.1/24 interface=VLAN30 network=10.30.30.0
/ip dhcp-client
add disabled=no interface=ether1-WAN
/ip dhcp-server network
add address=10.10.10.0/24 gateway=10.10.10.1
add address=10.20.20.0/24 gateway=10.20.20.1
add address=10.30.30.0/24 gateway=10.30.30.1
add address=172.16.16.0/24 gateway=172.16.16.1
/ip firewall nat
add action=masquerade chain=srcnat out-interface=ether1-WAN
/lcd interface pages
set 0 interfaces="ether1-WAN,ether2-direct-notSwitched,ether3-Link1of2,ether4-\
Link2of2,ether5-vlan-open,ether6-vlan30,ether7-vlan-PC,ether8-vlan-raspber\
ry,sfp1"
/system clock
set time-zone-name=Europe/Bratislava
/system identity
set name=GW
/system logging
add topics=caps
AP1 (RB952Ui):
# jan/02/1970 00:12:35 by RouterOS 6.47.4
# software id = HEJX-IA0M
#
# model = RB952Ui-5ac2nD
# serial number = 9E940A0DF21C
/interface bridge
add name=bridge1 vlan-filtering=yes
/interface wireless
# managed by CAPsMAN
# channel: 2412/20-Ce/gn(18dBm), SSID: WiFiWork, local forwarding
set [ find default-name=wlan1 ] disabled=no ssid=MikroTik
set [ find default-name=wlan2 ] ssid=MikroTik
/interface wireless security-profiles
set [ find default=yes ] supplicant-identity=MikroTik
/interface bridge port
add bridge=bridge1 interface=ether1
/interface bridge vlan
add bridge=bridge1 tagged=ether1 vlan-ids=30
/interface wireless cap
#
set bridge=bridge1 discovery-interfaces=bridge1 enabled=yes interfaces=wlan1